1
00:00:00,000 --> 00:00:00,670


2
00:00:00,670 --> 00:00:03,890
We have this system of equations, y is equal to 4x

3
00:00:03,890 --> 00:00:08,439
minus 17.5, and y plus 2x is equal to 6.5.

4
00:00:08,439 --> 00:00:10,149
And we have to solve for x and y.

5
00:00:10,150 --> 00:00:12,949
So we're looking for x's and y's that satisfy

6
00:00:12,949 --> 00:00:15,459
both of these equations.

7
00:00:15,460 --> 00:00:17,940
Now, the easiest way to think about it is we've already

8
00:00:17,940 --> 00:00:19,750
solved for y in this top equation.

9
00:00:19,750 --> 00:00:21,600
Let me write it again.

10
00:00:21,600 --> 00:00:22,800
I'll write it in pink.

11
00:00:22,800 --> 00:00:28,789
We have y is equal to 4x minus 17.5.

12
00:00:28,789 --> 00:00:31,189
So this first equation is telling us, literally, by this

13
00:00:31,190 --> 00:00:34,719
constraint, y should be 4 times x minus 17.5.

14
00:00:34,719 --> 00:00:37,939
Now, the second equation says whatever y is, we had 2 times

15
00:00:37,939 --> 00:00:40,070
x, and that should be 6.5.

16
00:00:40,070 --> 00:00:43,759
Well, the y here also has to meet this constraint up here.

17
00:00:43,759 --> 00:00:46,420
It also has to meet the constraint that it has to be 4

18
00:00:46,420 --> 00:00:49,530
times x minus 17.5.

19
00:00:49,530 --> 00:00:53,390
So what we can do is, is we can substitute this value for

20
00:00:53,390 --> 00:00:55,719
y into this equation.

21
00:00:55,719 --> 00:00:56,869
Let me be clear what I'm doing.

22
00:00:56,869 --> 00:01:04,179
The second equation here is y plus 2x is equal to 6.5.

23
00:01:04,180 --> 00:01:08,600
We know that y has to be equal to this thing right here. y

24
00:01:08,599 --> 00:01:12,869
has to be equal to 4x minus 17.5.

25
00:01:12,870 --> 00:01:19,790
So let's take 4x minus 17.5, and substitute y with that.

26
00:01:19,790 --> 00:01:21,320
So let's put that right there.

27
00:01:21,319 --> 00:01:24,239
So if we were to do that, if we were to replace this y with

28
00:01:24,239 --> 00:01:27,939
4x minus 17.5, because that's what the first equation is

29
00:01:27,939 --> 00:01:36,340
telling us, then we get 4x minus 17.5, plus

30
00:01:36,340 --> 00:01:39,810
2x is equal to 6.5.

31
00:01:39,810 --> 00:01:41,490
And now we have a single linear

32
00:01:41,489 --> 00:01:42,859
equation with one unknown.

33
00:01:42,859 --> 00:01:44,439
Let's solve for x.

34
00:01:44,439 --> 00:01:47,129
So first we have our x terms. We have a 4x,

35
00:01:47,129 --> 00:01:48,319
and we have a 2x.

36
00:01:48,319 --> 00:01:50,209
We can group them or add them together.

37
00:01:50,209 --> 00:01:53,399
4x plus 2x is 6x.

38
00:01:53,400 --> 00:02:03,510
And then we have 6x minus 17.5 is equal to 6.5.

39
00:02:03,510 --> 00:02:06,630
Then we can get the 17.5 out of the way by adding it to

40
00:02:06,629 --> 00:02:07,849
both sides of the equation.

41
00:02:07,849 --> 00:02:13,019
So this is negative 17.5, so let's add positive 17.5 to

42
00:02:13,020 --> 00:02:15,390
both sides of this equation.

43
00:02:15,389 --> 00:02:18,559
And we are left with the left-hand side is just going

44
00:02:18,560 --> 00:02:22,020
to be 6x, because these guys cancel out.

45
00:02:22,020 --> 00:02:27,480
6x is going to be equal to-- and 6.5-- see, 6 plus 17 is

46
00:02:27,479 --> 00:02:30,009
23, and then 0.5 plus 0.5 is 1.

47
00:02:30,009 --> 00:02:32,179
So this is going to be 24.

48
00:02:32,180 --> 00:02:34,670
And then we can divide both sides of this equation by 6.

49
00:02:34,669 --> 00:02:37,389


50
00:02:37,389 --> 00:02:42,250
And you are left with x is equal to 24 over 6, which is

51
00:02:42,250 --> 00:02:43,719
the same thing as 4.

52
00:02:43,719 --> 00:02:47,479
So we figured out the x value for the x and y pair that

53
00:02:47,479 --> 00:02:49,030
satisfy both of these equations.

54
00:02:49,030 --> 00:02:51,860
Now we need to figure out the y value.

55
00:02:51,860 --> 00:02:54,930
And we can do that by taking this x and putting it back

56
00:02:54,930 --> 00:02:56,180
into one of these equations.

57
00:02:56,180 --> 00:02:57,319
We can do it in to either one.

58
00:02:57,319 --> 00:02:58,965
We should get the same y value.

59
00:02:58,965 --> 00:03:01,450
So let's just do this top one up here.

60
00:03:01,449 --> 00:03:04,269
So if we assume x is equal to 4, this top equation tells us

61
00:03:04,270 --> 00:03:15,420
y is equal to 4 times x, which in this case is 4, minus 17.5.

62
00:03:15,419 --> 00:03:21,829
Well, this is equal to 16 minus 17.5, which is equal to

63
00:03:21,830 --> 00:03:23,610
negative 1.5.

64
00:03:23,610 --> 00:03:25,880
So y is equal to negative 1.5.

65
00:03:25,879 --> 00:03:31,819
So the solution to this system is x is equal to 4, y is equal

66
00:03:31,819 --> 00:03:34,620
to negative 1.5.

67
00:03:34,620 --> 00:03:37,539
And you can even verify that these two, they definitely

68
00:03:37,539 --> 00:03:41,039
work for the top one if you put 4 times 4, minus 17.5, you

69
00:03:41,039 --> 00:03:42,319
get negative 1.5.

70
00:03:42,319 --> 00:03:44,180
But they also work for the second one.

71
00:03:44,180 --> 00:03:45,290
And let's do that.

72
00:03:45,289 --> 00:03:49,900
In the second one, if you take negative 1.5, plus 2 times x--

73
00:03:49,900 --> 00:03:54,069
plus 2 times 4-- what does that equal?

74
00:03:54,069 --> 00:03:57,590
That's negative 1.5 plus 8.

75
00:03:57,590 --> 00:04:00,740
Well, negative 1.5 plus 8 is 6.5.

76
00:04:00,740 --> 00:04:04,969
So this x and y satisfy both of these equations.

77
00:04:04,969 --> 00:04:05,532