1
00:00:00,467 --> 00:00:06,600
Use substitution to solve for x and y they give us a system of equations here y is equal to negative

2
00:00:06,600 --> 00:00:14,333
five x plus 8 and ten x plus two y is equal to negative two so they've set it up for us pretty well they

3
00:00:14,333 --> 00:00:18,924
already have y specifically solved for up here so they tell us this first constraint tells us that y

4
00:00:18,924 --> 00:00:25,333
must be equal to negative five x plus eight so when we go to the second constraint here everytime we

5
00:00:25,333 --> 00:00:32,067
see a y we say well the first constraint tells us that y must be equal to negative five x plus eight

6
00:00:32,067 --> 00:00:38,867
so everywhere we see a y we can substitute it with negative five x plus 8 cuz thats what the first

7
00:00:38,867 --> 00:00:43,000
constraint tells us y is equal to that i dont want to be repetitive but i really want you to internalize

8
00:00:43,000 --> 00:00:48,267
thats all its saying y is that so everytime we see a y in the second constraint we can substitute it

9
00:00:48,267 --> 00:00:56,067
with that so lets do it so the second equation over here is ten x plus two and instead of writing a y

10
00:00:56,067 --> 00:01:01,267
there and ive said it multiple times already we can write a negative five x plus eight the first constraint

11
00:01:01,267 --> 00:01:11,133
tells us thats what y is so negative five x plus eight is equal to negative two now we have one equation

12
00:01:11,133 --> 00:01:19,200
with one unknown we can just solve for x we have ten x plus so we can multiply it we can distribute this

13
00:01:19,200 --> 00:01:28,933
two into both of these terms so we have two times negative five x is negative ten x and then two

14
00:01:28,933 --> 00:01:37,533
times eight is sixteen so plus sixteen is equal to negative two now we have ten x minus ten x those

15
00:01:37,533 --> 00:01:44,000
guys cancel out ten x minus ten x is equal to zero so these guys cancel out and we're just left with

16
00:01:44,000 --> 00:01:52,600
sixteen equals negative two which is crazy we know that sixteen does not equal negative two this is an

17
00:01:52,600 --> 00:01:59,327
inconsistent result and thats because these two lines actually dont intersect and we could see that

18
00:01:59,327 --> 00:02:04,333
by actually graphing these lines whenever you get something like some number equaling some other number

19
00:02:04,333 --> 00:02:09,467
that they're clearly not equal to that means its an inconsistent result its an inconsistent system and

20
00:02:09,467 --> 00:02:15,733
that these lines actually dont intersect so let me just graph these just to make it clear this first

21
00:02:15,733 --> 00:02:24,000
equation is already in slope y intercept form so it looks something like this thats our x axis this is

22
00:02:24,000 --> 00:02:32,467
our y axis and its negative five x plus eight so one two three four five six seven eight and then it

23
00:02:32,467 --> 00:02:38,667
has a very steep mega downward slope every time you move forward one you have to go down five so it

24
00:02:38,667 --> 00:02:43,800
looks something like that thats this first equation right over there the second equation let me re write

25
00:02:43,800 --> 00:02:50,800
it in slope y intercept form so its ten x plus two y is equal to negative two lets subract ten x from

26
00:02:50,800 --> 00:02:58,667
both sides you get two y is equal to negative ten x minus two lets divide both sides by two you get y

27
00:02:58,667 --> 00:03:05,600
is equal to negative five x negative five x minus one so its y intercept is negative one its right over

28
00:03:05,600 --> 00:03:11,867
there and it has the same slope as this first line so it looks like this its parallel its just shifted

29
00:03:11,867 --> 00:03:17,867
down a bit so it just looks like that so they're parallel lines they have the same slope different y

30
00:03:17,867 --> 00:03:26,541
intercept we get an inconsistent result they dont intersect and the tell tale sign of that when you're

31
00:03:26,541 --> 00:03:31,533
doing it algebraically is you get something wacky like this that is why its called inconsistent its not

32
00:03:31,533 --> 00:03:38,430
consistent for sixteen to be equal to negative two these dont intersect there's no solution to both of

33
00:03:38,430 --> 00:03:42,430
these constraints there's no x and y that satisfies both of them.