Use the elimination method to solve the following system of equations.
9x - 7y = 22
x + 3y = -24
To use the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.
First, let's multiply the second equation by 7 to make the coefficients of y the same:
7(x + 3y) = 7(-24)
7x + 21y = -168
Now, we have:
9x - 7y = 22
7x + 21y = -168
Now, add the two equations:
(9x + 7x) + (-7y + 21y) = 22 - 168
16x + 14y = -146
Now we have one equation with one variable:
16x + 14y = -146
Now, we can solve for x:
16x + 14y = -146
16x = -146 - 14y
x = (-146 - 14y) / 16
Now we can substitute this value of x back into either of the original equations to solve for y. Let's use the second equation:
x + 3y = -24
((-146 - 14y) / 16) + 3y = -24
-146 - 14y + 48y = -384
-146 + 34y = -384
34y = -238
y = -7
Now that we have y = -7, we can substitute this back into the second equation to find x:
x + 3(-7) = -24
x - 21 = -24
x = -24 + 21
x = -3
Therefore, the solution to the system of equations is x = -3, y = -7.