[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.63,0:00:06.27,Default,,0000,0000,0000,,The purpose of this video is to\Nlook at the solution of
Dialogue: 0,0:00:06.27,0:00:07.05,Default,,0000,0000,0000,,elementary simultaneous
Dialogue: 0,0:00:07.05,0:00:12.88,Default,,0000,0000,0000,,equations. Before we do that,\Nlet's just have a look at a
Dialogue: 0,0:00:12.88,0:00:13.73,Default,,0000,0000,0000,,relatively straightforward
Dialogue: 0,0:00:13.73,0:00:20.16,Default,,0000,0000,0000,,single equation. Equation we're\Ngoing to look at 2X minus
Dialogue: 0,0:00:20.16,0:00:21.90,Default,,0000,0000,0000,,Y equals 3.
Dialogue: 0,0:00:22.90,0:00:26.65,Default,,0000,0000,0000,,This is a linear equation. It's\Na linear equation because there
Dialogue: 0,0:00:26.65,0:00:31.77,Default,,0000,0000,0000,,are no terms in it that are X\Nsquared, Y squared or X times by
Dialogue: 0,0:00:31.77,0:00:36.54,Default,,0000,0000,0000,,Y or indeed ex cubes. The only\Nterms we've got a terms in X
Dialogue: 0,0:00:36.54,0:00:38.59,Default,,0000,0000,0000,,terms in Y and some numbers.
Dialogue: 0,0:00:39.70,0:00:42.78,Default,,0000,0000,0000,,So this represents a linear
Dialogue: 0,0:00:42.78,0:00:48.26,Default,,0000,0000,0000,,equation. We can rearrange it so\Nthat it says why equal
Dialogue: 0,0:00:48.26,0:00:53.33,Default,,0000,0000,0000,,something, so let's just do\Nthat. We can add Y to each side
Dialogue: 0,0:00:53.33,0:00:55.28,Default,,0000,0000,0000,,so that we get 2X.
Dialogue: 0,0:00:55.96,0:01:01.03,Default,,0000,0000,0000,,Equals 3 plus Yi. Did say add\Nwhy two each side and you might
Dialogue: 0,0:01:01.03,0:01:05.01,Default,,0000,0000,0000,,have wondered what happened\Nhere. Well, if I've got minus Y
Dialogue: 0,0:01:05.01,0:01:10.08,Default,,0000,0000,0000,,and I add why to it, I end up\Nwith no wise at all.
Dialogue: 0,0:01:11.40,0:01:18.41,Default,,0000,0000,0000,,Here we've got two X equals 3\Nplus Y, so let's take the three
Dialogue: 0,0:01:18.41,0:01:22.92,Default,,0000,0000,0000,,away from each side. 2X minus\Nthree equals Y.
Dialogue: 0,0:01:23.70,0:01:29.56,Default,,0000,0000,0000,,So there I've got a nice\Nexpression for why. If I take
Dialogue: 0,0:01:29.56,0:01:36.88,Default,,0000,0000,0000,,any value of X. Let's say I take\NX equals 1, then why will be
Dialogue: 0,0:01:36.88,0:01:44.20,Default,,0000,0000,0000,,equal to two times by 1 - 3,\Nwhich gives us minus one. So for
Dialogue: 0,0:01:44.20,0:01:51.03,Default,,0000,0000,0000,,this value of XI, get that value\Nof Yi can take another value of
Dialogue: 0,0:01:51.03,0:01:53.96,Default,,0000,0000,0000,,XX equals 2, Y will equal.
Dialogue: 0,0:01:54.02,0:01:58.34,Default,,0000,0000,0000,,2 * 2 - 3, which is\Nplus one.
Dialogue: 0,0:02:00.72,0:02:06.24,Default,,0000,0000,0000,,Another value of XX equals\N0 Y equals 2 times by 0 -
Dialogue: 0,0:02:06.24,0:02:11.77,Default,,0000,0000,0000,,3 will 2 * 0 is 0 and that\Ngives me minus three.
Dialogue: 0,0:02:13.28,0:02:17.92,Default,,0000,0000,0000,,So for every value of XI can\Ngenerate a value of Y.
Dialogue: 0,0:02:19.26,0:02:24.08,Default,,0000,0000,0000,,I can plot these as point\Nso I can plot this as the
Dialogue: 0,0:02:24.08,0:02:29.65,Default,,0000,0000,0000,,.1 - 1 and I can plot this\None on a graph as the .21
Dialogue: 0,0:02:29.65,0:02:34.10,Default,,0000,0000,0000,,and this one on a graph as\Nthe point nort minus three.
Dialogue: 0,0:02:34.10,0:02:36.33,Default,,0000,0000,0000,,So let's just set that up.
Dialogue: 0,0:02:39.70,0:02:40.83,Default,,0000,0000,0000,,Pair of axes.
Dialogue: 0,0:02:43.56,0:02:47.73,Default,,0000,0000,0000,,Let's mark the values of X that\Nwe've been having a look at.
Dialogue: 0,0:02:49.61,0:02:53.38,Default,,0000,0000,0000,,So that was X on there and why
Dialogue: 0,0:02:53.38,0:02:57.37,Default,,0000,0000,0000,,there? And let's put on the\Nvalues of why that we got.
Dialogue: 0,0:02:59.65,0:03:06.07,Default,,0000,0000,0000,,When X was zero hour value\Nof why was minus three?
Dialogue: 0,0:03:06.91,0:03:08.77,Default,,0000,0000,0000,,So that's. There.
Dialogue: 0,0:03:10.50,0:03:13.98,Default,,0000,0000,0000,,When X was one hour value was
Dialogue: 0,0:03:13.98,0:03:19.98,Default,,0000,0000,0000,,minus one. And when X was\Ntwo hour value was one.
Dialogue: 0,0:03:21.43,0:03:25.81,Default,,0000,0000,0000,,Those three points lie on\Na straight line.
Dialogue: 0,0:03:27.78,0:03:32.90,Default,,0000,0000,0000,,Y equals 2X minus three, and\Nthat's another reason for
Dialogue: 0,0:03:32.90,0:03:38.53,Default,,0000,0000,0000,,calling this a linear equation.\NIt gives us a straight line.
Dialogue: 0,0:03:39.65,0:03:40.36,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:03:42.19,0:03:49.61,Default,,0000,0000,0000,,You've got that one. Y equals 2X\Nminus three. Supposing we take a
Dialogue: 0,0:03:49.61,0:03:57.04,Default,,0000,0000,0000,,second one 3X plus two Y equals\N8, a second linear equation, and
Dialogue: 0,0:03:57.04,0:03:59.89,Default,,0000,0000,0000,,supposing we say these two.
Dialogue: 0,0:04:00.92,0:04:03.39,Default,,0000,0000,0000,,Are true at the same time.
Dialogue: 0,0:04:05.32,0:04:06.48,Default,,0000,0000,0000,,What does that mean?
Dialogue: 0,0:04:07.06,0:04:11.18,Default,,0000,0000,0000,,Well, we can plot this as a\Nstraight line. Again, it's a
Dialogue: 0,0:04:11.18,0:04:15.29,Default,,0000,0000,0000,,linear equation, so it's going\Nto give us a straight line. Now
Dialogue: 0,0:04:15.29,0:04:20.09,Default,,0000,0000,0000,,I don't want to have to workout\Nlots of points for this, So what
Dialogue: 0,0:04:20.09,0:04:24.90,Default,,0000,0000,0000,,I'm going to do is just sketch\Nit in quickly on the graph. I'm
Dialogue: 0,0:04:24.90,0:04:27.30,Default,,0000,0000,0000,,going to say when X is 0.
Dialogue: 0,0:04:27.91,0:04:32.88,Default,,0000,0000,0000,,And cover up the Exterm 2 Y is\Nequal to 8, so why must be
Dialogue: 0,0:04:32.88,0:04:36.52,Default,,0000,0000,0000,,equal to four which is going\Nto be up there somewhere?
Dialogue: 0,0:04:38.03,0:04:45.20,Default,,0000,0000,0000,,And when? Why is 03 X is equal\Nto 8 and so X is 8 / 3
Dialogue: 0,0:04:45.20,0:04:50.27,Default,,0000,0000,0000,,which gives us 2 and 2/3. So\Nsomewhere about their two 2/3
Dialogue: 0,0:04:50.27,0:04:55.75,Default,,0000,0000,0000,,and we know it's a straight\Nline, so we can get that by
Dialogue: 0,0:04:55.75,0:04:57.02,Default,,0000,0000,0000,,joining up there.
Dialogue: 0,0:04:58.40,0:05:05.48,Default,,0000,0000,0000,,This is the equation 3X plus two\NY equals 8. So what does it mean
Dialogue: 0,0:05:05.48,0:05:12.09,Default,,0000,0000,0000,,for these two to be true at the\Nsame time? Well, it must mean
Dialogue: 0,0:05:12.09,0:05:13.98,Default,,0000,0000,0000,,it's this point here.
Dialogue: 0,0:05:14.56,0:05:19.76,Default,,0000,0000,0000,,Where the two lines cross. So\Nwhen we solve a pair of
Dialogue: 0,0:05:19.76,0:05:23.22,Default,,0000,0000,0000,,simultaneous equations, what\Nwe're actually looking for is
Dialogue: 0,0:05:23.22,0:05:25.82,Default,,0000,0000,0000,,the intersection of two\Nstraight lines.
Dialogue: 0,0:05:26.85,0:05:32.43,Default,,0000,0000,0000,,Of course, it could happen that\Nwe have one line like that.
Dialogue: 0,0:05:33.40,0:05:34.83,Default,,0000,0000,0000,,And apparel line.
Dialogue: 0,0:05:35.97,0:05:37.22,Default,,0000,0000,0000,,They would never meet.
Dialogue: 0,0:05:38.17,0:05:42.19,Default,,0000,0000,0000,,And one of the examples that\Nwe're going to be looking at
Dialogue: 0,0:05:42.19,0:05:45.54,Default,,0000,0000,0000,,later will show what happens\Nin terms of the arithmetic
Dialogue: 0,0:05:45.54,0:05:49.22,Default,,0000,0000,0000,,when we have this particular\Ncase. But for now, let's go
Dialogue: 0,0:05:49.22,0:05:52.91,Default,,0000,0000,0000,,back and think about these\Ntwo. How can we handle these
Dialogue: 0,0:05:52.91,0:05:56.60,Default,,0000,0000,0000,,two algebraically so that we\Ndon't have to draw graphs? We
Dialogue: 0,0:05:56.60,0:05:59.61,Default,,0000,0000,0000,,don't have to rely on\Nsketching, we can calculate
Dialogue: 0,0:05:59.61,0:06:02.96,Default,,0000,0000,0000,,which is so much easier in\Nmost cases that actually
Dialogue: 0,0:06:02.96,0:06:03.96,Default,,0000,0000,0000,,drawing a graph.
Dialogue: 0,0:06:05.25,0:06:08.87,Default,,0000,0000,0000,,So let's take these two\Nequations.
Dialogue: 0,0:06:12.85,0:06:18.20,Default,,0000,0000,0000,,And we're going to look at two\Nmethods of solution, so I'm
Dialogue: 0,0:06:18.20,0:06:23.11,Default,,0000,0000,0000,,going to look at method one.\NNow, let's begin with the
Dialogue: 0,0:06:23.11,0:06:28.91,Default,,0000,0000,0000,,original equation that we had\Ntwo X minus. Y is equal to three
Dialogue: 0,0:06:28.91,0:06:35.60,Default,,0000,0000,0000,,and then the one that we put\Nwith it 3X plus two Y equals 8.
Dialogue: 0,0:06:37.36,0:06:41.73,Default,,0000,0000,0000,,Our first method of solution,\Nwell, one of the things to do is
Dialogue: 0,0:06:41.73,0:06:46.10,Default,,0000,0000,0000,,to do what we did in the very\Nfirst case with this and
Dialogue: 0,0:06:46.10,0:06:48.78,Default,,0000,0000,0000,,Rearrange one of these\Nequations. It doesn't matter
Dialogue: 0,0:06:48.78,0:06:50.80,Default,,0000,0000,0000,,which one, but we'll take this
Dialogue: 0,0:06:50.80,0:06:54.76,Default,,0000,0000,0000,,one. So that we get Y
Dialogue: 0,0:06:54.76,0:07:01.42,Default,,0000,0000,0000,,equals. And we know what the\Nresult for that one is. It's Y
Dialogue: 0,0:07:01.42,0:07:03.15,Default,,0000,0000,0000,,equals 2X minus three.
Dialogue: 0,0:07:05.23,0:07:07.52,Default,,0000,0000,0000,,So that's equation one.
Dialogue: 0,0:07:08.17,0:07:15.72,Default,,0000,0000,0000,,That's equation. Two, so this\Nis now, let's call it equation 3
Dialogue: 0,0:07:15.72,0:07:18.87,Default,,0000,0000,0000,,and we got it by rearranging.
Dialogue: 0,0:07:21.15,0:07:21.94,Default,,0000,0000,0000,,1.
Dialogue: 0,0:07:23.61,0:07:29.32,Default,,0000,0000,0000,,What we're going to do with this\Nis if these two have to be true
Dialogue: 0,0:07:29.32,0:07:33.52,Default,,0000,0000,0000,,at the same time, then this\Nrelationship must be true in
Dialogue: 0,0:07:33.52,0:07:37.33,Default,,0000,0000,0000,,this equation, so we can\Nsubstitute it in, so let's.
Dialogue: 0,0:07:38.35,0:07:40.99,Default,,0000,0000,0000,,Substitute 3
Dialogue: 0,0:07:42.46,0:07:48.82,Default,,0000,0000,0000,,until two so we\Nhave 3X plus.
Dialogue: 0,0:07:50.29,0:07:58.22,Default,,0000,0000,0000,,Two times Y. But why is\N2X minus three that's equal to
Dialogue: 0,0:07:58.22,0:08:02.51,Default,,0000,0000,0000,,8? And you can see that what\Nwe've done is we've reduced.
Dialogue: 0,0:08:03.19,0:08:08.48,Default,,0000,0000,0000,,This. To this equation giving us\Na single equation in one
Dialogue: 0,0:08:08.48,0:08:12.58,Default,,0000,0000,0000,,unknown, which is a simple\Nlinear equation and we can solve
Dialogue: 0,0:08:12.58,0:08:19.92,Default,,0000,0000,0000,,it. Multiply out the brackets 3X\Nplus 4X minus 6 equals 8.
Dialogue: 0,0:08:21.15,0:08:26.69,Default,,0000,0000,0000,,Gather the excess together. 7X\Nminus 6 equals 8.
Dialogue: 0,0:08:27.47,0:08:33.45,Default,,0000,0000,0000,,At the six to each side, Seven X\Nequals 14, and so X must be 2.
Dialogue: 0,0:08:35.02,0:08:37.09,Default,,0000,0000,0000,,That's only given as one value.
Dialogue: 0,0:08:38.06,0:08:42.87,Default,,0000,0000,0000,,We need a value of Y, but up\Nhere we've got an expression
Dialogue: 0,0:08:42.87,0:08:48.05,Default,,0000,0000,0000,,which says Y equals and if we\Ntake the value of X that we've
Dialogue: 0,0:08:48.05,0:08:49.53,Default,,0000,0000,0000,,got and substituted in.
Dialogue: 0,0:08:50.42,0:08:55.03,Default,,0000,0000,0000,,Therefore, why\Nwill be equal to 2
Dialogue: 0,0:08:55.03,0:08:58.99,Default,,0000,0000,0000,,* 2 - 3 gives US1?
Dialogue: 0,0:09:00.60,0:09:05.47,Default,,0000,0000,0000,,And so we've got a solution X\Nequals 2, Y equals 1.
Dialogue: 0,0:09:06.91,0:09:08.28,Default,,0000,0000,0000,,Are we sure it's right?
Dialogue: 0,0:09:09.04,0:09:13.89,Default,,0000,0000,0000,,Well, we used this equation\Nwhich came from equation one to
Dialogue: 0,0:09:13.89,0:09:16.10,Default,,0000,0000,0000,,generate the value of Y.
Dialogue: 0,0:09:16.74,0:09:22.27,Default,,0000,0000,0000,,So if we take the values of X&Y\Nand put them back into here,
Dialogue: 0,0:09:22.27,0:09:27.01,Default,,0000,0000,0000,,they should work, should give us\Nthe right answer. So let's try
Dialogue: 0,0:09:27.01,0:09:28.59,Default,,0000,0000,0000,,that. X is 2.
Dialogue: 0,0:09:29.35,0:09:37.04,Default,,0000,0000,0000,,3 times by two is 6 plus, Y is\N1 two times by one is 2 six and
Dialogue: 0,0:09:37.04,0:09:42.16,Default,,0000,0000,0000,,two gives us eight. Yes, this\Nworks. This is a solution of
Dialogue: 0,0:09:42.16,0:09:47.71,Default,,0000,0000,0000,,that equation and of that one.\NSo this is our answer to the
Dialogue: 0,0:09:47.71,0:09:49.42,Default,,0000,0000,0000,,pair of simultaneous equations.
Dialogue: 0,0:09:50.32,0:09:54.49,Default,,0000,0000,0000,,Let's have a look at another one\Nusing this particular method.
Dialogue: 0,0:09:57.42,0:10:00.04,Default,,0000,0000,0000,,The example we're going to use\Nis going to be said.
Dialogue: 0,0:10:00.11,0:10:07.20,Default,,0000,0000,0000,,Open X. +2\NY equals 47 and
Dialogue: 0,0:10:07.20,0:10:13.92,Default,,0000,0000,0000,,five X minus four\NY equals 1.
Dialogue: 0,0:10:15.93,0:10:21.29,Default,,0000,0000,0000,,Now. We need to make a choice.\NWe need to choose one of these
Dialogue: 0,0:10:21.29,0:10:27.50,Default,,0000,0000,0000,,two equations. And Rearrange it\Nso that it says Y equals or if
Dialogue: 0,0:10:27.50,0:10:29.24,Default,,0000,0000,0000,,we want X equals.
Dialogue: 0,0:10:31.19,0:10:35.74,Default,,0000,0000,0000,,The choice is entirely ours and\Nwe have to make the choice based
Dialogue: 0,0:10:35.74,0:10:40.29,Default,,0000,0000,0000,,upon what we feel will be the\Nsimplest and looking at a pair
Dialogue: 0,0:10:40.29,0:10:44.14,Default,,0000,0000,0000,,of equations like this often\Ndifficult to know which is the
Dialogue: 0,0:10:44.14,0:10:47.64,Default,,0000,0000,0000,,simplest. Well, let's pick at\Nrandom. Let's choose this one
Dialogue: 0,0:10:47.64,0:10:51.49,Default,,0000,0000,0000,,and let's Rearrange Equation\Ntoo. So we'll start by getting X
Dialogue: 0,0:10:51.49,0:10:56.74,Default,,0000,0000,0000,,equals this time. So we say 5X\Nis equal to 1 and I'm going to
Dialogue: 0,0:10:56.74,0:10:59.54,Default,,0000,0000,0000,,add 4 Y to each side plus 4Y.
Dialogue: 0,0:11:00.58,0:11:04.76,Default,,0000,0000,0000,,Now I'm going to divide\Nthroughout by the five so that I
Dialogue: 0,0:11:04.76,0:11:10.49,Default,,0000,0000,0000,,have. X on its own. Now I've got\Nto divide everything by 5.
Dialogue: 0,0:11:11.13,0:11:15.07,Default,,0000,0000,0000,,Everything so I had to put\Nthat line there to show that
Dialogue: 0,0:11:15.07,0:11:19.33,Default,,0000,0000,0000,,I'm dividing the one and the\Nfour Y. So this is a fraction.
Dialogue: 0,0:11:19.33,0:11:24.25,Default,,0000,0000,0000,,I'm sure you can tell this is\Nnot going to be as easy as the
Dialogue: 0,0:11:24.25,0:11:27.53,Default,,0000,0000,0000,,previous question was. In\Nfact, it's going to be quite
Dialogue: 0,0:11:27.53,0:11:31.14,Default,,0000,0000,0000,,difficult because I have to\Ntake this now and because it
Dialogue: 0,0:11:31.14,0:11:32.45,Default,,0000,0000,0000,,came from equation too.
Dialogue: 0,0:11:37.66,0:11:42.63,Default,,0000,0000,0000,,I'm going to have to take it and\Nsubstitute it back into equation
Dialogue: 0,0:11:42.63,0:11:47.59,Default,,0000,0000,0000,,one, and this isn't looking very\Npretty, so let's give it a try
Dialogue: 0,0:11:47.59,0:11:49.46,Default,,0000,0000,0000,,sub. 3.
Dialogue: 0,0:11:51.18,0:11:59.00,Default,,0000,0000,0000,,Until one. So I\Nhave 7X but X is this
Dialogue: 0,0:11:59.00,0:12:06.09,Default,,0000,0000,0000,,lump of algebra here 1 +\N4 Y all over 5.
Dialogue: 0,0:12:06.73,0:12:10.50,Default,,0000,0000,0000,,+2 Y equals
Dialogue: 0,0:12:10.50,0:12:15.60,Default,,0000,0000,0000,,47. I can see this is\Nbecoming quite horrific.
Dialogue: 0,0:12:16.62,0:12:20.55,Default,,0000,0000,0000,,Multiply throughout by 5 why?\NBecause we're dividing by 5. We
Dialogue: 0,0:12:20.55,0:12:25.54,Default,,0000,0000,0000,,want to get rid of the fraction.\NThe way to do that is to
Dialogue: 0,0:12:25.54,0:12:30.19,Default,,0000,0000,0000,,multiply everything by 5 and it\Nhas to be everything. So if we
Dialogue: 0,0:12:30.19,0:12:34.83,Default,,0000,0000,0000,,multiply that by 5 because we're\Ndividing by 5, it's as though we
Dialogue: 0,0:12:34.83,0:12:41.25,Default,,0000,0000,0000,,actually do nothing to the 1 + 4\NY. That leaves a 7 * 1 + 4 Y.
Dialogue: 0,0:12:41.91,0:12:47.68,Default,,0000,0000,0000,,We need five times that that's\Nten Y and we have to have five
Dialogue: 0,0:12:47.68,0:12:51.39,Default,,0000,0000,0000,,times that remember, an\Nequation is a balance. What
Dialogue: 0,0:12:51.39,0:12:57.15,Default,,0000,0000,0000,,you do to one side of the\Nbalance you have to do to the
Dialogue: 0,0:12:57.15,0:13:00.45,Default,,0000,0000,0000,,other. If you don't, it's\Nunbalanced. So we're
Dialogue: 0,0:13:00.45,0:13:05.39,Default,,0000,0000,0000,,multiplying everything by 5.\NSo 5 * 47 five 735, five falls
Dialogue: 0,0:13:05.39,0:13:06.63,Default,,0000,0000,0000,,of 22135 altogether.
Dialogue: 0,0:13:07.77,0:13:15.39,Default,,0000,0000,0000,,Now we need to multiply out the\Nbrackets 7 + 28 Y plus 10
Dialogue: 0,0:13:15.39,0:13:19.19,Default,,0000,0000,0000,,Y equals 235. So we take this
Dialogue: 0,0:13:19.19,0:13:23.69,Default,,0000,0000,0000,,equation. Write it down again so\Nthat we can see it clearly.
Dialogue: 0,0:13:30.92,0:13:35.24,Default,,0000,0000,0000,,Now we can gather these two\Ntogether gives us 38Y.
Dialogue: 0,0:13:36.31,0:13:41.92,Default,,0000,0000,0000,,And we can take Seven away\Nfrom each side, which will
Dialogue: 0,0:13:41.92,0:13:43.45,Default,,0000,0000,0000,,give us 228.
Dialogue: 0,0:13:44.91,0:13:49.83,Default,,0000,0000,0000,,Exactly big numbers coming in\Nhere 228 / 38 'cause we're
Dialogue: 0,0:13:49.83,0:13:54.74,Default,,0000,0000,0000,,looking for the number which\Nwhen we multiplied by 38 will
Dialogue: 0,0:13:54.74,0:13:57.87,Default,,0000,0000,0000,,give us 228 and that's going to
Dialogue: 0,0:13:57.87,0:14:03.02,Default,,0000,0000,0000,,be 6. So we've established Y is\Nequal to 6.
Dialogue: 0,0:14:03.95,0:14:09.20,Default,,0000,0000,0000,,Having done that, we can take it\Nand we can substitute it back
Dialogue: 0,0:14:09.20,0:14:14.45,Default,,0000,0000,0000,,into the equation that we first\Nhad for X. So remember that for
Dialogue: 0,0:14:14.45,0:14:17.28,Default,,0000,0000,0000,,that we had X was equal to.
Dialogue: 0,0:14:18.10,0:14:25.30,Default,,0000,0000,0000,,And what we had for that was 1\N+ 4 Y all over five. We
Dialogue: 0,0:14:25.30,0:14:32.02,Default,,0000,0000,0000,,substitute in the six, so we\Nhave 1 + 24 or over 5 and
Dialogue: 0,0:14:32.02,0:14:39.22,Default,,0000,0000,0000,,quickly we can see that's 25 /\N5. So we have X equals 5. So
Dialogue: 0,0:14:39.22,0:14:44.98,Default,,0000,0000,0000,,again we've got our pair of\Nvalues. Our answer to the pair
Dialogue: 0,0:14:44.98,0:14:48.82,Default,,0000,0000,0000,,of simultaneous equations. We\Nhaven't checked it though.
Dialogue: 0,0:14:49.39,0:14:53.84,Default,,0000,0000,0000,,Now remember that this came from\Nthe second equation, so really
Dialogue: 0,0:14:53.84,0:14:59.52,Default,,0000,0000,0000,,to check it we've got to go back\Nto the very first equation that
Dialogue: 0,0:14:59.52,0:15:05.18,Default,,0000,0000,0000,,we had written down that one. If\Nyou remember was Seven X +2, Y
Dialogue: 0,0:15:05.18,0:15:06.80,Default,,0000,0000,0000,,is equal to 47.
Dialogue: 0,0:15:07.88,0:15:15.34,Default,,0000,0000,0000,,So let's just check 7 *\N5. That gives us 35 +
Dialogue: 0,0:15:15.34,0:15:17.21,Default,,0000,0000,0000,,2 * 6.
Dialogue: 0,0:15:17.90,0:15:23.34,Default,,0000,0000,0000,,That gives us 12, so we 35 + 12\Nequals 47. And yes, that is what
Dialogue: 0,0:15:23.34,0:15:28.10,Default,,0000,0000,0000,,we wanted, so we now know that\Nthis is correct, but I just stop
Dialogue: 0,0:15:28.10,0:15:29.46,Default,,0000,0000,0000,,and think about it.
Dialogue: 0,0:15:30.04,0:15:34.88,Default,,0000,0000,0000,,We got all those fractions to\Nwork with. We got this lump of
Dialogue: 0,0:15:34.88,0:15:39.71,Default,,0000,0000,0000,,algebra to carry around with us.\NIs there not an easier way of
Dialogue: 0,0:15:39.71,0:15:44.82,Default,,0000,0000,0000,,doing these? Yes there is. It's\Nuseful to have seen the method
Dialogue: 0,0:15:44.82,0:15:49.76,Default,,0000,0000,0000,,that we have got simply because\Nwe will need it again when we
Dialogue: 0,0:15:49.76,0:15:53.18,Default,,0000,0000,0000,,look at the second video of\Nsimultaneous equations, but.
Dialogue: 0,0:15:54.03,0:15:58.57,Default,,0000,0000,0000,,That is a simple way of handling\Nthese, so let's go on now and
Dialogue: 0,0:15:58.57,0:16:00.51,Default,,0000,0000,0000,,have a look at method 2.
Dialogue: 0,0:16:09.30,0:16:12.85,Default,,0000,0000,0000,,Now this method is sometimes\Ncalled elimination and we can
Dialogue: 0,0:16:12.85,0:16:17.46,Default,,0000,0000,0000,,see why it gets that name and\Nthis is the method that you
Dialogue: 0,0:16:17.46,0:16:21.37,Default,,0000,0000,0000,,really do need to practice and\Nbecome accustomed to. So let's
Dialogue: 0,0:16:21.37,0:16:24.92,Default,,0000,0000,0000,,start with the same equations\Nthat we had last time.
Dialogue: 0,0:16:26.00,0:16:26.98,Default,,0000,0000,0000,,And see.
Dialogue: 0,0:16:28.54,0:16:32.63,Default,,0000,0000,0000,,How it works and how much easier\Nit actually is?
Dialogue: 0,0:16:33.78,0:16:37.32,Default,,0000,0000,0000,,OK method of elimination. What\Ndo we do?
Dialogue: 0,0:16:38.18,0:16:42.43,Default,,0000,0000,0000,,What we do is we seek\Nto make the
Dialogue: 0,0:16:42.43,0:16:45.26,Default,,0000,0000,0000,,coefficients in front\Nof the wise.
Dialogue: 0,0:16:46.41,0:16:48.57,Default,,0000,0000,0000,,Or in front of the axes.
Dialogue: 0,0:16:49.43,0:16:50.21,Default,,0000,0000,0000,,The same.
Dialogue: 0,0:16:51.65,0:16:56.09,Default,,0000,0000,0000,,Once we've gotten the same,\Nthen we can either add the
Dialogue: 0,0:16:56.09,0:16:59.33,Default,,0000,0000,0000,,two equations together or\Nsubtract them according to
Dialogue: 0,0:16:59.33,0:17:01.35,Default,,0000,0000,0000,,the signs that are there.
Dialogue: 0,0:17:02.78,0:17:08.30,Default,,0000,0000,0000,,By doing that, we will get rid\Nof that particular unknown, the
Dialogue: 0,0:17:08.30,0:17:10.14,Default,,0000,0000,0000,,one that we chose.
Dialogue: 0,0:17:10.75,0:17:14.31,Default,,0000,0000,0000,,To make the coefficients\Nnumerically the same.
Dialogue: 0,0:17:15.72,0:17:18.89,Default,,0000,0000,0000,,So. This one what would we do?
Dialogue: 0,0:17:19.56,0:17:22.73,Default,,0000,0000,0000,,Well, if we look at this and
Dialogue: 0,0:17:22.73,0:17:28.91,Default,,0000,0000,0000,,this. Here we have two Y and\Nhere we have minus four Y.
Dialogue: 0,0:17:29.54,0:17:34.40,Default,,0000,0000,0000,,So if I were to double that, I'd\Nhave four. Why there? And it's
Dialogue: 0,0:17:34.40,0:17:38.91,Default,,0000,0000,0000,,plus four Y Ana minus four Y\Nthere, and that seems are pretty
Dialogue: 0,0:17:38.91,0:17:43.42,Default,,0000,0000,0000,,good thing to do, because then\Nthey're both for Y. One of them
Dialogue: 0,0:17:43.42,0:17:47.93,Default,,0000,0000,0000,,is plus and one of them is\Nminus. And if I add them
Dialogue: 0,0:17:47.93,0:17:51.75,Default,,0000,0000,0000,,together they will disappear. So\Nlet me just number the equations
Dialogue: 0,0:17:51.75,0:17:52.79,Default,,0000,0000,0000,,one and two.
Dialogue: 0,0:17:53.65,0:17:59.05,Default,,0000,0000,0000,,And then I can keep a record of\Nwhat I'm doing. So I'm going to
Dialogue: 0,0:17:59.05,0:18:03.01,Default,,0000,0000,0000,,multiply the first equation by\Ntwo and that's going to lead
Dialogue: 0,0:18:03.01,0:18:05.17,Default,,0000,0000,0000,,Maine to a new equation 3.
Dialogue: 0,0:18:05.78,0:18:07.00,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:18:07.82,0:18:14.79,Default,,0000,0000,0000,,2 * 7 X is 14X\Nplus two times, that is 4
Dialogue: 0,0:18:14.79,0:18:21.18,Default,,0000,0000,0000,,Y equals 2 times that, and\N2 * 47 is 94.
Dialogue: 0,0:18:22.19,0:18:27.95,Default,,0000,0000,0000,,Now equation two. I'm leaving as\Nit is not going to touch it.
Dialogue: 0,0:18:30.51,0:18:32.62,Default,,0000,0000,0000,,Now I've got two equations.
Dialogue: 0,0:18:34.11,0:18:41.19,Default,,0000,0000,0000,,This is plus four Y and this\Nis minus four Y. So if I
Dialogue: 0,0:18:41.19,0:18:47.27,Default,,0000,0000,0000,,add the two equations together,\Nwhat happens? I get 14X plus 5X.
Dialogue: 0,0:18:47.27,0:18:48.78,Default,,0000,0000,0000,,That's 19 X.
Dialogue: 0,0:18:50.88,0:18:56.78,Default,,0000,0000,0000,,No whys. 'cause I've plus four Y\Nadd it to minus four Y know wise
Dialogue: 0,0:18:56.78,0:18:57.95,Default,,0000,0000,0000,,at all equals.
Dialogue: 0,0:18:58.82,0:18:59.85,Default,,0000,0000,0000,,95
Dialogue: 0,0:19:01.01,0:19:06.39,Default,,0000,0000,0000,,and so X is 95 over 19, which\Ngives me 5 which if you
Dialogue: 0,0:19:06.39,0:19:10.23,Default,,0000,0000,0000,,remember, is the answer we have\Nto the last question.
Dialogue: 0,0:19:11.82,0:19:15.28,Default,,0000,0000,0000,,Now we need to take this and\Nsubstitute it back. Doesn't
Dialogue: 0,0:19:15.28,0:19:18.44,Default,,0000,0000,0000,,matter which equation we choose\Nto substitute it back into.
Dialogue: 0,0:19:18.44,0:19:19.70,Default,,0000,0000,0000,,Let's take this one.
Dialogue: 0,0:19:20.35,0:19:27.56,Default,,0000,0000,0000,,X is 5, so five times\Nby 5 - 4 Y equals
Dialogue: 0,0:19:27.56,0:19:28.16,Default,,0000,0000,0000,,1.
Dialogue: 0,0:19:29.20,0:19:35.09,Default,,0000,0000,0000,,And so we have 25 -\N4 Y equals 1.
Dialogue: 0,0:19:37.20,0:19:39.93,Default,,0000,0000,0000,,Take the four way over\Nto that side by adding
Dialogue: 0,0:19:39.93,0:19:41.30,Default,,0000,0000,0000,,four Y to each side.
Dialogue: 0,0:19:43.26,0:19:49.12,Default,,0000,0000,0000,,So that will give us 25 is equal\Nto four Y plus one. Take the one
Dialogue: 0,0:19:49.12,0:19:54.97,Default,,0000,0000,0000,,away from its side, 24 is 4 Y\Nand so why is equal to 6 and
Dialogue: 0,0:19:54.97,0:19:58.100,Default,,0000,0000,0000,,we've got exactly the same\Nanswer as we had before. And
Dialogue: 0,0:19:58.100,0:20:00.10,Default,,0000,0000,0000,,let's just look.
Dialogue: 0,0:20:01.40,0:20:05.43,Default,,0000,0000,0000,,How much simpler that is? How\Nmuch quicker that answer came
Dialogue: 0,0:20:05.43,0:20:09.82,Default,,0000,0000,0000,,out. One thing to notice. Well,\Ntwo things in actual fact. First
Dialogue: 0,0:20:09.82,0:20:14.21,Default,,0000,0000,0000,,of all, I try to keep the equal\Nsigns underneath each other.
Dialogue: 0,0:20:15.06,0:20:19.25,Default,,0000,0000,0000,,This is not only makes it look\Nneat, it enables you to see what
Dialogue: 0,0:20:19.25,0:20:20.44,Default,,0000,0000,0000,,it is you're doing.
Dialogue: 0,0:20:21.54,0:20:25.08,Default,,0000,0000,0000,,Keep the equations together so\Nthe setting out of this work
Dialogue: 0,0:20:25.08,0:20:27.34,Default,,0000,0000,0000,,actually helps you to be able to
Dialogue: 0,0:20:27.34,0:20:32.78,Default,,0000,0000,0000,,check it. Second thing to notice\Nis down this side. I've kept a
Dialogue: 0,0:20:32.78,0:20:36.89,Default,,0000,0000,0000,,record of exactly what I've done\Nmultiplying the equation by two,
Dialogue: 0,0:20:36.89,0:20:39.87,Default,,0000,0000,0000,,adding the two equations\Ntogether. That's very helpful
Dialogue: 0,0:20:39.87,0:20:45.09,Default,,0000,0000,0000,,when you want to check your\Nwork. What did I do? How did I
Dialogue: 0,0:20:45.09,0:20:48.82,Default,,0000,0000,0000,,actually work this out? By\Nhaving this record down the
Dialogue: 0,0:20:48.82,0:20:53.67,Default,,0000,0000,0000,,side, you don't have to work it\Nout again. You can see exactly
Dialogue: 0,0:20:53.67,0:20:58.52,Default,,0000,0000,0000,,what it is that you did. Now\Nlet's take a third example and
Dialogue: 0,0:20:58.52,0:21:03.22,Default,,0000,0000,0000,,again. Will solve it by means of\Nthe method of elimination. Just
Dialogue: 0,0:21:03.22,0:21:08.65,Default,,0000,0000,0000,,so we've got a second example of\Nthat method to look at three X
Dialogue: 0,0:21:08.65,0:21:10.98,Default,,0000,0000,0000,,+7 Y is 27 and 5X.
Dialogue: 0,0:21:12.62,0:21:14.97,Default,,0000,0000,0000,,+2 Y is 60.
Dialogue: 0,0:21:16.43,0:21:20.23,Default,,0000,0000,0000,,OK, we've got a choice to make.\NWe can make either the
Dialogue: 0,0:21:20.23,0:21:23.72,Default,,0000,0000,0000,,coefficients in front of the axe\Nnumerically the same, or the
Dialogue: 0,0:21:23.72,0:21:27.52,Default,,0000,0000,0000,,coefficients in front of the\Nwise. Well, in order to do that,
Dialogue: 0,0:21:27.52,0:21:31.01,Default,,0000,0000,0000,,I'd have to multiply the Y.\NCertainly have to multiply this
Dialogue: 0,0:21:31.01,0:21:35.45,Default,,0000,0000,0000,,equation by two to give me 14\Nthere and this one by 7:00 to
Dialogue: 0,0:21:35.45,0:21:36.72,Default,,0000,0000,0000,,give me 14 there.
Dialogue: 0,0:21:38.31,0:21:39.93,Default,,0000,0000,0000,,How do I make that choice? Well?
Dialogue: 0,0:21:40.99,0:21:45.74,Default,,0000,0000,0000,,Fairly clearly 2 times by 7 is\N14, so 1 by 1, one by the other.
Dialogue: 0,0:21:46.66,0:21:49.92,Default,,0000,0000,0000,,But I don't really like\Nmultiplying by 7 difficult
Dialogue: 0,0:21:49.92,0:21:54.26,Default,,0000,0000,0000,,number. I prefer to multiply by\Nthree and five, so my choices
Dialogue: 0,0:21:54.26,0:21:58.24,Default,,0000,0000,0000,,actually governed by how well I\Nthink I can handle the
Dialogue: 0,0:21:58.24,0:22:02.59,Default,,0000,0000,0000,,arithmetic. So let's multiply\Nthis one by 5 and this one by
Dialogue: 0,0:22:02.59,0:22:06.57,Default,,0000,0000,0000,,three will give us 15X an 15X\Nnumber. The equations one.
Dialogue: 0,0:22:08.24,0:22:14.92,Default,,0000,0000,0000,,2. And I'll take equation one\Nand I will multiply it by 5 and
Dialogue: 0,0:22:14.92,0:22:17.80,Default,,0000,0000,0000,,that will give me a new equation
Dialogue: 0,0:22:17.80,0:22:24.08,Default,,0000,0000,0000,,3. So multiplying\Nit by 5:15
Dialogue: 0,0:22:24.08,0:22:30.15,Default,,0000,0000,0000,,X plus 35\NY is equal
Dialogue: 0,0:22:30.15,0:22:36.38,Default,,0000,0000,0000,,to 135. And then\Nequation two, I will multiply by
Dialogue: 0,0:22:36.38,0:22:40.79,Default,,0000,0000,0000,,three and that will give me a\Nnew equation for.
Dialogue: 0,0:22:41.61,0:22:46.05,Default,,0000,0000,0000,,Oh, here we go. Multiplying this\Nby three 15X.
Dialogue: 0,0:22:46.75,0:22:52.06,Default,,0000,0000,0000,,Plus six Y is\Nequal to 48.
Dialogue: 0,0:22:53.52,0:22:59.87,Default,,0000,0000,0000,,These are now both 15X and\Nthey're both plus 15X.
Dialogue: 0,0:23:00.56,0:23:06.32,Default,,0000,0000,0000,,So if I take this equation away\Nfrom that equation, I'll have
Dialogue: 0,0:23:06.32,0:23:13.04,Default,,0000,0000,0000,,15X minus 15X no X is at all.\NI live eliminative, the X, I'll
Dialogue: 0,0:23:13.04,0:23:18.80,Default,,0000,0000,0000,,just have the Wise left, so\Nlet's do that equation 3 minus
Dialogue: 0,0:23:18.80,0:23:25.40,Default,,0000,0000,0000,,equation 4. 15X takeaway\N15X no axis 35 Y
Dialogue: 0,0:23:25.40,0:23:30.96,Default,,0000,0000,0000,,takeaway six Y that gives\Nus 29 Y.
Dialogue: 0,0:23:32.25,0:23:38.66,Default,,0000,0000,0000,,And then 135 takeaway 48?\NAnd that's going to give us
Dialogue: 0,0:23:38.66,0:23:45.08,Default,,0000,0000,0000,,A7 their 87 altogether. And\Nso why is 87 over 29,
Dialogue: 0,0:23:45.08,0:23:47.41,Default,,0000,0000,0000,,which gives us 3?
Dialogue: 0,0:23:48.60,0:23:55.41,Default,,0000,0000,0000,,Having got that, I need to know\Nthe value of X so I can take
Dialogue: 0,0:23:55.41,0:24:00.86,Default,,0000,0000,0000,,Y equals 3 and substituted back\Nlet's say into equation one. So
Dialogue: 0,0:24:00.86,0:24:08.12,Default,,0000,0000,0000,,I have 3X plus Seven times Y 7\Nthrees are 21 is equal to 27 and
Dialogue: 0,0:24:08.12,0:24:14.02,Default,,0000,0000,0000,,so 3X is 6 taking 21 away from\Neach side and access 2.
Dialogue: 0,0:24:15.53,0:24:21.80,Default,,0000,0000,0000,,Check this in here 5 twos are\Nten 2306 ten and six gives me 16
Dialogue: 0,0:24:21.80,0:24:27.65,Default,,0000,0000,0000,,which is what I want so I know\Nthat this is my answer. My
Dialogue: 0,0:24:27.65,0:24:31.41,Default,,0000,0000,0000,,solution to this pair of\Nsimultaneous equations and again
Dialogue: 0,0:24:31.41,0:24:35.59,Default,,0000,0000,0000,,look how straightforward that\Nis. Much, much easier than the
Dialogue: 0,0:24:35.59,0:24:40.19,Default,,0000,0000,0000,,first method that we saw. Also\Nthink about using letters as
Dialogue: 0,0:24:40.19,0:24:44.79,Default,,0000,0000,0000,,well. If we've got letters to\Nuse instead of coefficients the
Dialogue: 0,0:24:44.79,0:24:50.10,Default,,0000,0000,0000,,numbers here. So we might have a\NX plus BY. Again, this is a much
Dialogue: 0,0:24:50.10,0:24:53.44,Default,,0000,0000,0000,,better method to use. Again,\Nnotice the setting down keeping
Dialogue: 0,0:24:53.44,0:24:56.80,Default,,0000,0000,0000,,it compact, keeping the equal\Nsigns under each other and
Dialogue: 0,0:24:56.80,0:25:00.82,Default,,0000,0000,0000,,keeping a record of what we've\Ndone. So do something comes out
Dialogue: 0,0:25:00.82,0:25:04.16,Default,,0000,0000,0000,,wrong, we can check it, see what\Nwe are doing.
Dialogue: 0,0:25:05.13,0:25:09.30,Default,,0000,0000,0000,,Now all the examples that we've\Nlooked at so far of all had
Dialogue: 0,0:25:09.30,0:25:12.51,Default,,0000,0000,0000,,whole number coefficients. They\Nmight have been, plus they might
Dialogue: 0,0:25:12.51,0:25:15.72,Default,,0000,0000,0000,,be minus, but they've been whole\Nnumber, and everything that
Dialogue: 0,0:25:15.72,0:25:19.90,Default,,0000,0000,0000,,we've looked at as being in this\Nsort of form XY number XY
Dialogue: 0,0:25:19.90,0:25:23.43,Default,,0000,0000,0000,,number. Well, not all equations\Ncome like that, so let's just
Dialogue: 0,0:25:23.43,0:25:25.67,Default,,0000,0000,0000,,have a look at a couple of
Dialogue: 0,0:25:25.67,0:25:29.26,Default,,0000,0000,0000,,examples that. Don't look like\Nthe ones we've just done.
Dialogue: 0,0:25:31.37,0:25:36.32,Default,,0000,0000,0000,,First of all, let's have this\NOne X equals 3 Y.
Dialogue: 0,0:25:37.00,0:25:42.92,Default,,0000,0000,0000,,And X over 3 minus Y equals\N34 pair of simultaneous
Dialogue: 0,0:25:42.92,0:25:47.22,Default,,0000,0000,0000,,equations. Linear simultaneous\Nequations again 'cause they both
Dialogue: 0,0:25:47.22,0:25:53.68,Default,,0000,0000,0000,,got just X&Y in an numbers,\Nnothing else, no X squared's now
Dialogue: 0,0:25:53.68,0:25:55.29,Default,,0000,0000,0000,,ex wise etc.
Dialogue: 0,0:25:56.03,0:26:01.98,Default,,0000,0000,0000,,We need to get them into a form\Nthat we can use and that would
Dialogue: 0,0:26:01.98,0:26:07.54,Default,,0000,0000,0000,,be nice to have XY number. So\Nlet's do that with this One X
Dialogue: 0,0:26:07.54,0:26:12.31,Default,,0000,0000,0000,,equals 3 Y, so will have X minus\Nthree Y equals 0.
Dialogue: 0,0:26:13.99,0:26:18.68,Default,,0000,0000,0000,,This one got a fraction in it.\NFractions we don't like, can't
Dialogue: 0,0:26:18.68,0:26:22.59,Default,,0000,0000,0000,,handle fractions. Let's get rid\Nof the three by multiplying
Dialogue: 0,0:26:22.59,0:26:26.89,Default,,0000,0000,0000,,everything in this equation by\Nthree. So will do that three
Dialogue: 0,0:26:26.89,0:26:29.63,Default,,0000,0000,0000,,times X over 3 just leaves us
Dialogue: 0,0:26:29.63,0:26:37.12,Default,,0000,0000,0000,,with X. Three times the Y\Nminus three Y equals 3 times.
Dialogue: 0,0:26:37.12,0:26:40.08,Default,,0000,0000,0000,,This going to be 102.
Dialogue: 0,0:26:42.28,0:26:42.97,Default,,0000,0000,0000,,Problem.
Dialogue: 0,0:26:44.92,0:26:48.67,Default,,0000,0000,0000,,These two bits here are exactly
Dialogue: 0,0:26:48.67,0:26:52.41,Default,,0000,0000,0000,,the same. But these two\Nbits are different.
Dialogue: 0,0:26:54.14,0:26:55.93,Default,,0000,0000,0000,,What's going to happen?
Dialogue: 0,0:26:56.80,0:27:00.22,Default,,0000,0000,0000,,Well, clearly if we subtract\Nthese two equations one from
Dialogue: 0,0:27:00.22,0:27:03.64,Default,,0000,0000,0000,,the other, there won't be\Nanything left this side when
Dialogue: 0,0:27:03.64,0:27:06.72,Default,,0000,0000,0000,,we've done the subtraction X\Nfrom X, no access.
Dialogue: 0,0:27:07.75,0:27:11.53,Default,,0000,0000,0000,,Minus 3 Y takeaway minus three\NY know why is left, and yet
Dialogue: 0,0:27:11.53,0:27:15.32,Default,,0000,0000,0000,,we're going to have 0 - 102\Nequals minus 102 at this side.
Dialogue: 0,0:27:15.32,0:27:17.94,Default,,0000,0000,0000,,In other words, we're gonna\Nend up with that.
Dialogue: 0,0:27:21.21,0:27:22.94,Default,,0000,0000,0000,,Which is a wee bit strange.
Dialogue: 0,0:27:23.89,0:27:27.13,Default,,0000,0000,0000,,What's the problem? What's the\Ndifficulty? Remember right back
Dialogue: 0,0:27:27.13,0:27:30.73,Default,,0000,0000,0000,,at the beginning when we drew a\Ncouple of graphs?
Dialogue: 0,0:27:32.10,0:27:37.14,Default,,0000,0000,0000,,In the first case we had two\Nlines that actually crossed, but
Dialogue: 0,0:27:37.14,0:27:41.76,Default,,0000,0000,0000,,in the second case I drew 2\Nlines that were parallel.
Dialogue: 0,0:27:42.51,0:27:47.57,Default,,0000,0000,0000,,And that's exactly what we've\Ngot here. We have got 2 lines
Dialogue: 0,0:27:47.57,0:27:51.79,Default,,0000,0000,0000,,that are parallel because\Nthey've got this same form. They
Dialogue: 0,0:27:51.79,0:27:56.86,Default,,0000,0000,0000,,are parallel lines so they don't\Nmeet. And what this is telling
Dialogue: 0,0:27:56.86,0:28:01.92,Default,,0000,0000,0000,,us is there in fact is no\Nsolution to this pair of
Dialogue: 0,0:28:01.92,0:28:06.56,Default,,0000,0000,0000,,equations because they come from\N2 parallel lines that do not
Dialogue: 0,0:28:06.56,0:28:11.21,Default,,0000,0000,0000,,meet no solution. There isn't\None fixed point, so we would
Dialogue: 0,0:28:11.21,0:28:12.47,Default,,0000,0000,0000,,write that down.
Dialogue: 0,0:28:12.58,0:28:15.48,Default,,0000,0000,0000,,Simply say no solutions.
Dialogue: 0,0:28:17.66,0:28:19.66,Default,,0000,0000,0000,,And it's important to keep\Nan eye out for that.
Dialogue: 0,0:28:20.74,0:28:24.63,Default,,0000,0000,0000,,Check back, make sure the\Narithmetic's correct yes, but do
Dialogue: 0,0:28:24.63,0:28:26.19,Default,,0000,0000,0000,,remember that can happen.
Dialogue: 0,0:28:27.14,0:28:33.72,Default,,0000,0000,0000,,Let's take just one more final\Nexample, X over 5.
Dialogue: 0,0:28:35.34,0:28:38.65,Default,,0000,0000,0000,,Minus Y over 4 equals 0.
Dialogue: 0,0:28:40.20,0:28:47.89,Default,,0000,0000,0000,,3X plus 1/2 Y equals\N70. Now for this one.
Dialogue: 0,0:28:48.80,0:28:52.17,Default,,0000,0000,0000,,We've got fractions with\Ndominators five and four, and we
Dialogue: 0,0:28:52.17,0:28:56.21,Default,,0000,0000,0000,,need to get rid of those. So we\Nneed a common denominator.
Dialogue: 0,0:28:57.05,0:29:01.16,Default,,0000,0000,0000,,With which we can multiply\Neverything in the equation and
Dialogue: 0,0:29:01.16,0:29:06.91,Default,,0000,0000,0000,,those get rid of the five in the\Nfall. The obvious one to choose
Dialogue: 0,0:29:06.91,0:29:13.08,Default,,0000,0000,0000,,is 20, because 20 is 5 times by\N4. Let us write that down in
Dialogue: 0,0:29:13.08,0:29:18.83,Default,,0000,0000,0000,,falls 20 times X over 5 - 20\Ntimes Y over 4 equals 0
Dialogue: 0,0:29:18.83,0:29:21.71,Default,,0000,0000,0000,,be'cause. 20 * 0 is still 0.
Dialogue: 0,0:29:23.05,0:29:29.21,Default,,0000,0000,0000,,Little bit of counseling 5\Ninto 20 goes 4.
Dialogue: 0,0:29:30.05,0:29:33.63,Default,,0000,0000,0000,,4 into 20 goes 5.
Dialogue: 0,0:29:34.70,0:29:40.21,Default,,0000,0000,0000,,So we have 4X minus five\NY equals 0.
Dialogue: 0,0:29:42.00,0:29:46.71,Default,,0000,0000,0000,,So that was our first equation\Nthat was our second equation.
Dialogue: 0,0:29:46.71,0:29:51.84,Default,,0000,0000,0000,,This one is now become our third\Nequation. So equation one has
Dialogue: 0,0:29:51.84,0:29:53.56,Default,,0000,0000,0000,,gone to equation 3.
Dialogue: 0,0:29:54.43,0:29:57.42,Default,,0000,0000,0000,,Let's look at equation two. Now\Nthat we need to deal with it,
Dialogue: 0,0:29:57.42,0:29:59.49,Default,,0000,0000,0000,,it's got a half way in it. So if
Dialogue: 0,0:29:59.49,0:30:03.63,Default,,0000,0000,0000,,I multiply every. Anything by\Ntwo. This will become just why?
Dialogue: 0,0:30:04.35,0:30:05.95,Default,,0000,0000,0000,,So we have 6X.
Dialogue: 0,0:30:06.83,0:30:13.98,Default,,0000,0000,0000,,Plus Y equals 34 and so\Nequation two has become. Now
Dialogue: 0,0:30:13.98,0:30:19.24,Default,,0000,0000,0000,,equation for. We want to\Neliminate one of the variables
Dialogue: 0,0:30:19.24,0:30:24.05,Default,,0000,0000,0000,,OK, which one well I'd have to\Ndo quite a bit of multiplication
Dialogue: 0,0:30:24.05,0:30:30.34,Default,,0000,0000,0000,,by 6:00 AM by 4. If it was, the\Nex is that I wanted to get rid
Dialogue: 0,0:30:30.34,0:30:35.15,Default,,0000,0000,0000,,of look, there's a minus five\Nhere and one there, so to speak.
Dialogue: 0,0:30:35.15,0:30:39.96,Default,,0000,0000,0000,,So if we multiply this one by\Nfive, will get these two the
Dialogue: 0,0:30:39.96,0:30:45.14,Default,,0000,0000,0000,,same. So let's do that 4X minus\Nfive Y equals 0, and then times
Dialogue: 0,0:30:45.14,0:30:46.62,Default,,0000,0000,0000,,in this by 5.
Dialogue: 0,0:30:46.93,0:30:54.08,Default,,0000,0000,0000,,30X plus five Y equals and then\Nwe do this by 5, five, 420, not
Dialogue: 0,0:30:54.08,0:31:01.24,Default,,0000,0000,0000,,down and two to carry 5 threes\Nare 15 and the two is 17, so
Dialogue: 0,0:31:01.24,0:31:07.92,Default,,0000,0000,0000,,that gives us 170 and now we can\Njust add these two together. So
Dialogue: 0,0:31:07.92,0:31:13.64,Default,,0000,0000,0000,,equation three state as it was\Nequation for we multiplied by 5.
Dialogue: 0,0:31:13.64,0:31:16.98,Default,,0000,0000,0000,,So that's gone to equation 5 and
Dialogue: 0,0:31:16.98,0:31:21.92,Default,,0000,0000,0000,,now. Finally, we're going to\Nadd together equations three
Dialogue: 0,0:31:21.92,0:31:29.07,Default,,0000,0000,0000,,and five, and so we have 34\NX equals 170 and wise have
Dialogue: 0,0:31:29.07,0:31:30.17,Default,,0000,0000,0000,,been illuminated.
Dialogue: 0,0:31:33.76,0:31:41.75,Default,,0000,0000,0000,,34 X is 170 and so\NX is 170 / 34 and
Dialogue: 0,0:31:41.75,0:31:44.42,Default,,0000,0000,0000,,that gives us 5.
Dialogue: 0,0:31:45.43,0:31:50.05,Default,,0000,0000,0000,,We need to go back and\Nsubstituting to one of our two
Dialogue: 0,0:31:50.05,0:31:53.93,Default,,0000,0000,0000,,equations. It's just\Nhave a look which one?
Dialogue: 0,0:31:55.11,0:31:57.95,Default,,0000,0000,0000,,Doesn't really matter, I\Nthink. Actually choose to go
Dialogue: 0,0:31:57.95,0:32:02.06,Default,,0000,0000,0000,,for that one. Why? because I\Ncan see that five over 5 gives
Dialogue: 0,0:32:02.06,0:32:05.54,Default,,0000,0000,0000,,me one, and that's a very\Nsimple number. Might make the
Dialogue: 0,0:32:05.54,0:32:06.80,Default,,0000,0000,0000,,arithmetic so much easier.
Dialogue: 0,0:32:08.08,0:32:15.30,Default,,0000,0000,0000,,So we'll have X over 5 minus\NY. Over 4 equals 0. Take the
Dialogue: 0,0:32:15.30,0:32:17.37,Default,,0000,0000,0000,,Five and substituted in.
Dialogue: 0,0:32:21.52,0:32:27.90,Default,,0000,0000,0000,,5 over 5. That's just one, and\Nso I have one takeaway Y over 4
Dialogue: 0,0:32:27.90,0:32:33.84,Default,,0000,0000,0000,,equals 0, so one must be equal\Nto Y over 4. If I multiply
Dialogue: 0,0:32:33.84,0:32:38.94,Default,,0000,0000,0000,,everything by 4I end up with\Nfour equals Y. So there's my
Dialogue: 0,0:32:38.94,0:32:44.47,Default,,0000,0000,0000,,pair of answers X equals 5, Y\Nequals 4 and I really should
Dialogue: 0,0:32:44.47,0:32:48.72,Default,,0000,0000,0000,,just check by looking at the\Nsecond equation now, remember.
Dialogue: 0,0:32:49.05,0:32:54.12,Default,,0000,0000,0000,,2nd equation was 3X\Nplus 1/2 Y equals 17.
Dialogue: 0,0:32:55.69,0:32:59.10,Default,,0000,0000,0000,,3X also, half Y
Dialogue: 0,0:32:59.10,0:33:05.98,Default,,0000,0000,0000,,equals 17. So let's substitute\Nthese in. X is 5, three X is.
Dialogue: 0,0:33:05.98,0:33:11.78,Default,,0000,0000,0000,,Therefore AR15, three fives plus\N1/2 of Y. But why is 4 so 1/2
Dialogue: 0,0:33:11.78,0:33:18.01,Default,,0000,0000,0000,,of it is 2. That gives me 17,\Nwhich is what I want. Yes, this
Dialogue: 0,0:33:18.01,0:33:23.95,Default,,0000,0000,0000,,is correct. Let's just recap for\Na moment. Apparel simultaneous
Dialogue: 0,0:33:23.95,0:33:29.07,Default,,0000,0000,0000,,equations. They represent two\Nstraight lines in effect when we
Dialogue: 0,0:33:29.07,0:33:34.70,Default,,0000,0000,0000,,solve them together, we are\Nlooking for the point where the
Dialogue: 0,0:33:34.70,0:33:36.75,Default,,0000,0000,0000,,two straight lines intersect.
Dialogue: 0,0:33:38.87,0:33:43.02,Default,,0000,0000,0000,,The method of elimination is\Nmuch, much better to use than
Dialogue: 0,0:33:43.02,0:33:45.28,Default,,0000,0000,0000,,the first method that we saw.
Dialogue: 0,0:33:46.27,0:33:50.29,Default,,0000,0000,0000,,Remember also in the way that\Nwe've set this one out. Keep a
Dialogue: 0,0:33:50.29,0:33:52.45,Default,,0000,0000,0000,,record of what it is that you
Dialogue: 0,0:33:52.45,0:33:56.64,Default,,0000,0000,0000,,do. Set you workout so that the\Nequal signs come under each
Dialogue: 0,0:33:56.64,0:34:00.35,Default,,0000,0000,0000,,other and so that at a glance\Nyou can look at what you've
Dialogue: 0,0:34:00.35,0:34:01.50,Default,,0000,0000,0000,,done. Check your working.
Dialogue: 0,0:34:02.08,0:34:06.46,Default,,0000,0000,0000,,Finally, remember the answer\Nthat you get can always be
Dialogue: 0,0:34:06.46,0:34:10.84,Default,,0000,0000,0000,,checked by substituting the pair\Nof values into the equations
Dialogue: 0,0:34:10.84,0:34:15.66,Default,,0000,0000,0000,,that you began with. That means\Nstrictly you should never get
Dialogue: 0,0:34:15.66,0:34:19.16,Default,,0000,0000,0000,,one of these wrong. However,\Nmistakes do happen.