Use the elimination method to solve the follow system of equations.

Question

9x−7y=22


x+3y=−24


This question requires you to show your work.

(1 point)
Responses

(4, 2)
(4, 2)

(3,−9)
open paren 3 comma negative 9 close paren

(−3,−7)
open paren negative 3 comma negative 7 close paren

(0,−8)

Answer 1

First, let's multiply the second equation by 7 to match the coefficients of y in both equations:

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

Now we have:

9x - 7y = 22
7x + 21y = -168

Next, we can add the two equations together to eliminate y:

(9x - 7y) + (7x + 21y) = 22 - 168
16x + 14y = -146

Now we have:

16x + 14y = -146

To solve for x, we can divide this equation by 2:

8x + 7y = -73

Now we have a system of equations:

8x + 7y = -73
9x - 7y = 22

Adding both equations eliminates y:

8x + 7y + 9x - 7y = -73 + 22
17x = -51
x = -3

Now we can substitute x back into one of the original equations to find y:

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

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