Use the elimination method to solve the follow system of equations

Question

9x - 7y = 22
x + 3y = -24

Answer 1

First, we need to make the coefficients of one of the variables the same in both equations. Let's do this by multiplying the second equation by 7:

7(x + 3y) = 7(-24)
7x + 21y = -168

Now we have the system:
9x - 7y = 22
7x + 21y = -168

Add the two equations together:
(9x - 7y) + (7x + 21y) = 22 - 168
16x + 14y = -146

Divide by 2 to simplify:
8x + 7y = -73

Now we have:
8x + 7y = -73
9x - 7y = 22

Add the two equations together:
(8x + 7y) + (9x - 7y) = -73 + 22
17x = -51
x = -3

Now substitute x back into one of the equations to solve for y. Let's use the first equation:

-3 + 3y = -24
3y = -21
y = -7

Therefore, the solution to the system of equations is x = -3, y = -7.