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

9x−7y=22


x+3y=−24


This question requires you to show your work.

(1 point)
Responses

(4, 2)
(4, 2)

(0,−8)
open paren 0 comma negative 8 close paren

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

(−3,−7)

1 answer

To solve this system of equations using the elimination method, we can multiply the second equation by 7 to eliminate y.

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

Adding these two equations together, we get:

16x + 14y = -146
=> 8x + 7y = -73

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

Adding these two equations together, we get:

17x = -51
x = -51/17
x = -3

Substitute x = -3 into the first equation:
9(-3) - 7y = 22
-27 - 7y = 22
-7y = 49
y = -49/7
y = -7

Therefore, the solution to the system of equations is (-3, -7).