Use The Linear Combination Method To Solve The System Of Equations. Explain Each Step Of Your Solution. If Steps Are Not Explained, You Will Not Recei

Use the linear combination method to solve the system of equations. Explain each step of your solution. If steps are not explained, you will not receive credit for that step.

2x+9y= -26
-3x-7y=13

  Answer:

x = 5
y = -4

Explanation:

2x + 9y = -26
-3x - 7y = 13
___________

One of the variables should be cancelled
For that to happen the signs should be different and when you add it they will be cancelled
If you cant cancel any of them then you have to think what to MULTIPLY or what you should do to the equations

First, pick one of the variables that you want to cancel
So i want to cancel "x"
For that to happen i should think what to multiply to the equations for them to be cancelled
Im going to multiply them by 3 and 2

3(2x + 9y = -26)
2(-3x - 7y = 13)
___________

Then distribute them

6x + 27y = -78
-6x - 14y = 26
____________

You can cancel the "x" now and then add them

13y = -52

Divide 13 from both sides

13/13y = -52/13

Solve

y = -4

After getting the value of one of the variables substitute it to one of the equations to get the value of the other variable (you can choose any equation between the two of them)

2x + 9y = -26
2x + 9(-4) = - 26
2x - 36 = -26
Transpose - 36 and then change the sign
2x = -26 + 36
Compute them
2x = 10
Divide 2 from both sides
2/2x = 10/2
Solve
x = 5

_____CHECKING_____
2x + 9y = -26
2(5) + 9(-4) = -26
10 - 36 = -26
-26 = -26 TRUE

-3x - 7y = 13
-3(5) - 7(-4) = 13
-15 + 28 = 13
13 = 13 TRUE