Question

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

9x - 7y = 22
x + 3y = - 24

Answer 1

First, we can multiply the second equation by 9 so that the coefficients of x in both equations are the same:

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

Now, our system of equations is:

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

Next, we can subtract the first equation from the second equation:

(9x + 27y) - (9x - 7y) = -216 - 22
9x + 27y - 9x + 7y = -238
34y = -238
y = -7

Now that we have found the value of y, we can substitute it back into the second equation to find the value of x:

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

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