Use the elimination method to solve the follow system of equations.
9x−7y=22
x+3y=−24
show work
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
Now we can subtract the first equation from the second equation to eliminate x:
(9x + 27y) - (9x - 7y) = -216 - 22
9x + 27y - 9x + 7y = -238
34y = -238
y = -7
Now substitute y = -7 back into one of the original equations to solve for x:
x + 3(-7) = -24
x - 21 = -24
x = -3
Therefore, the solution to the system of equations is x = -3 and y = -7.