Question

Which ordered pair is the solution to the system of equations? x+y=-1 x- 3y=11 A. (2, −3) B. (−2, 1) C. (5, −2) D. (−6, 5)

Answer 1

will medal and fan

Answer 2

So. This Pre-Algebra?

Answer 3

ya im really bad at math

Answer 4

No your not. It's algebra few people actually understand it.

Answer 5

So their are two ways to do this. The cheaty way and the way you'll use if this was real life.

Answer 6

Let's do the later.

Answer 7

okay

Answer 8

So do you remember how to solve a system of equations?

Answer 9

no

Answer 10

mk fair enough. So what we have to do is substitute (Sorry for the delay haven't had to do this type of problem in a while had to get my brain remembering this).

Answer 11

its all good

Answer 12

We know that the values of x and y will be identical for both equations.

Answer 13

okay

Answer 14

x + y =-1
x - 3y =11
What that means is we have to take one these equations and substitute for x or y in the other equation. Or perhaps more simply we need to isolate one variable on one side and substitute the isolated variable for it in the other equation.

Answer 15

alright

Answer 16

Let's use the second equation since it isn't just the variables it has that lovely 3y.

Answer 17

k

Answer 18

So what we must do is cancel out 3y.

Answer 19

We do this by using the reverse of the number/variable.

Answer 20

If I had -3 for example what number would I have to add to get 0.

Answer 21

You there?

Answer 22

ya sry you add three

Answer 23

Exactly.

Answer 24

Any reverse of the same number always equals 0

Answer 25

yah

Answer 26

So -3y + 3y would equal 0. However due to the law of symmetry we must do it to both sides of the equation. So our second equation looks like this: x - 3y + 3y = 11 + 3y however since were canceling. We can safely remove the 3y's on the left side of the equation thus giving us x = 11 + 3y

Answer 27

Think you understand so far?

Answer 28

sorta

Answer 29

OK now here is the tricky part.

Answer 30

No we must take our second equation. and substitute it for x in the first equation.

Answer 31

mk

Answer 32

okay

Answer 33

Sorry I mean x + y = -1 is now 11 + 3y + y = -1

Typoed.

Answer 34

its ok

Answer 35

So now let's add like terms. 3y + y is equal to 4y.

Answer 36

So our equation is now 11 + 4y = -1

Answer 37

Now we do the same that did for the second equation. Think you can do this one?

Answer 38

so im going to add like nterms

Answer 39

No we've already done that. What were going to do is cancel out terms on the left side.

Answer 40

However. Keep in mind we do the reverse of PEMDAS

Answer 41

In other words we do addition and subtraction cancellation instead of multiplication and division cancellation first.

Answer 42

So we have 11 + 4y = -1 so let's get rid of 11 first.

Answer 43

subtract 11 from both sides and we get 11 - 11 + 3y = -1 - 11

Answer 44

or 4y = -12

Answer 45

my head just exploded

Answer 46

stay with me. Were almost done.

Answer 47

okay

Answer 48

Alright. So with 4y we are multiplying y 4 times. or in other words we have y + y + y + y

Answer 49

or rather adding y not multiplying.

Answer 50

So how do we cancel 4y.

Answer 51

we add 4y to both sides?

Answer 52

No we do not. What is the reverse of multiplication.

Answer 53

division

Answer 54

There you go. So our equation is 4y / 4y = -12 / 4y

Answer 55

or actually hang on a second. we don't divide by 4y that would just leave us with a 1 on the left side. What we do is is 4y / 4 = -12 / 4

Answer 56

Or in other words. y = -3

Answer 57

So now we know the value of y.

Answer 58

ok

Answer 59

Now we need to find the value of x. But since we know the value of y it will be a lot easier to find the value of x.

Answer 60

So we take any of the two equations (let's do the first one and substitute y for -3

Answer 61

x + y = -1 is now x + -3 = -1

Answer 62

We do cancellation one last time and we get x - 3 + 3 = -1 + 3

Answer 63

Or x = 2

Answer 64

and that is the awnser for your question. x = 2 and y = -3 or (2, -3).

Answer 65

I recommend bookmarking this page if you need a refresher for this.

Answer 66

okay thank you

Answer 67

It's a pleasure.