1
00:00:00,000 --> 00:00:00,450


2
00:00:00,450 --> 00:00:03,250
We're told to look at the coordinate grid above.

3
00:00:03,250 --> 00:00:04,830
I put it on the side here.

4
00:00:04,830 --> 00:00:07,599
Identify one system of two lines that

5
00:00:07,599 --> 00:00:09,910
has a single solution.

6
00:00:09,910 --> 00:00:12,689
Then identify one system of two lines that

7
00:00:12,689 --> 00:00:16,269
does not have a solution.

8
00:00:16,269 --> 00:00:18,655
So let's do the first part first. So a single solution.

9
00:00:18,655 --> 00:00:23,039


10
00:00:23,039 --> 00:00:26,369
And they say identify one system, but we can see here

11
00:00:26,370 --> 00:00:28,000
there's actually going to be two systems that

12
00:00:28,000 --> 00:00:29,649
have a single solution.

13
00:00:29,649 --> 00:00:32,228
And when we talk about a single solution, we're talking

14
00:00:32,228 --> 00:00:36,170
about a single x and y value that will satisfy both

15
00:00:36,170 --> 00:00:37,850
equations in the system.

16
00:00:37,850 --> 00:00:41,370
So if we look right here at the points of intersection,

17
00:00:41,369 --> 00:00:46,169
this point right there, that satisfies this equation y is

18
00:00:46,170 --> 00:00:48,969
equal to 0.1x plus 1.

19
00:00:48,969 --> 00:00:53,939
And it also satisfies, well, this blue line, but the graph

20
00:00:53,939 --> 00:00:58,179
that that line represents, y is equal to 4x plus 10.

21
00:00:58,179 --> 00:01:01,530
So this dot right here, that point represents a solution to

22
00:01:01,530 --> 00:01:02,460
both of these.

23
00:01:02,460 --> 00:01:04,950
Or I guess another way to think about it, it represents

24
00:01:04,950 --> 00:01:09,290
an x and y value that satisfy both of these constraints.

25
00:01:09,290 --> 00:01:12,890
So one system that has one solution is the system that

26
00:01:12,890 --> 00:01:19,879
has y is equal to 0.1x plus 1, and then this blue line right

27
00:01:19,879 --> 00:01:25,799
here, which is y is equal to 4x plus 10.

28
00:01:25,799 --> 00:01:28,019
Now, they only want us to identify one system of two

29
00:01:28,019 --> 00:01:29,649
lines that has a single solution.

30
00:01:29,650 --> 00:01:31,080
We've already done that.

31
00:01:31,079 --> 00:01:32,730
But just so you see it, there's actually another

32
00:01:32,730 --> 00:01:33,730
system here.

33
00:01:33,730 --> 00:01:37,380
So this is one system right here, or another system would

34
00:01:37,379 --> 00:01:40,129
be the green line and this red line.

35
00:01:40,129 --> 00:01:43,899
This point of intersection right here, once again, that

36
00:01:43,900 --> 00:01:47,740
represents an x and y value that satisfies both the

37
00:01:47,739 --> 00:01:56,929
equation y is equal to 0.1x plus 1, and this point right

38
00:01:56,930 --> 00:02:02,070
here satisfies the equation y is equal to 4x minus 6.

39
00:02:02,069 --> 00:02:05,239


40
00:02:05,239 --> 00:02:08,288
So if you look at this system, there's one solution, because

41
00:02:08,288 --> 00:02:11,019
there's one point of intersection of these two

42
00:02:11,020 --> 00:02:14,530
equations or these two lines, and this system also has one

43
00:02:14,530 --> 00:02:17,000
solution because it has one point of intersection.

44
00:02:17,000 --> 00:02:19,509
Now, the second part of the problem, they say identify one

45
00:02:19,509 --> 00:02:22,949
system of two lines that does not have a single solution or

46
00:02:22,949 --> 00:02:24,739
does not have a solution, so no solution.

47
00:02:24,740 --> 00:02:27,689


48
00:02:27,689 --> 00:02:30,180
So in order for there to be no solution, that means that the

49
00:02:30,180 --> 00:02:34,840
two constraints don't overlap, that there's no point that is

50
00:02:34,840 --> 00:02:39,659
common to both equations or there's no pair of x, y values

51
00:02:39,659 --> 00:02:41,359
that's common to both equations.

52
00:02:41,360 --> 00:02:44,840
And that's the case of the two parallel lines here, this blue

53
00:02:44,840 --> 00:02:46,229
line and this green line.

54
00:02:46,229 --> 00:02:50,409
Because they never intersect, there's no coordinate on the

55
00:02:50,409 --> 00:02:52,949
coordinate plane that satisfies both equations.

56
00:02:52,949 --> 00:02:56,419
So there's no x and y that satisfy both.

57
00:02:56,419 --> 00:02:59,379
So the second part of the question, a system that has no

58
00:02:59,379 --> 00:03:05,449
solution is y is equal to 4x plus 10, and then the other

59
00:03:05,449 --> 00:03:12,250
one is y is equal to 4x minus 6.

60
00:03:12,250 --> 00:03:17,680
And notice, they have the exact same slope, and they're

61
00:03:17,680 --> 00:03:20,270
two different lines, they have different intercepts, so they

62
00:03:20,270 --> 00:03:22,659
never, ever intersect, and that's why

63
00:03:22,659 --> 00:03:24,599
they have no solutions.

64
00:03:24,599 --> 00:03:25,265