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

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

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

(4, 2)
(4, 2)

(3,−9)

1 answer

First, multiply the second equation by 9 to make the coefficients of x the same:

9(x + 3y) = 9(-24)
9x + 27y = -216

Now, we have the system of equations:

9x - 7y = 22
9x + 27y = -216

Add the two equations together to eliminate x:

(9x - 7y) + (9x + 27y) = 22 - 216
18x + 20y = -194

Now, divide by 2 to simplify:

9x + 10y = -97

Now we have two equations:

9x - 7y = 22
9x + 10y = -97

Add these equations together to eliminate x:

(9x - 7y) + (9x + 10y) = 22 - 97
18x + 3y = -75

Divide by 3 to simplify:

6x + y = -25

Now, we have the equations:

6x + y = -25
9x - 7y = 22

Multiplying the first equation by 7 and the second equation by 1, we get:

42x + 7y = -175
9x - 7y = 22

Adding these equations together:

51x = -153
x = -3

Substitute x = -3 into one of the original equations:

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

Therefore, the solution is (x, y) = (-3, -7).