Use the elimination method to solve the follow system of equations.%0D%0A%0D%0A9x−7y=22%0D%0A9%0D%0A%0D%0A−%0D%0A7%0D%0A%0D%0A=%0D%0A22%0D%0A %0D%0A%0D%0Ax+3y=−24
To solve the system of equations using the elimination method, we need to multiply one or both of the equations by a constant such that the coefficients of x (or y) in the two equations are additive inverses.
Given the system of equations:
1) 9x - 7y = 22
2) x + 3y = -24
Let's multiply equation 2 by 9 to make the coefficient of x in equation 1 equal to 9:
9(x + 3y) = 9(-24)
9x + 27y = -216
Now, the equations are:
1) 9x - 7y = 22
2) 9x + 27y = -216
Now, let's subtract equation 1 from equation 2:
(9x + 27y) - (9x - 7y) = -216 - 22
9x + 27y - 9x + 7y = -238
34y = -238
y = -238 / 34
y = -7
Now that we have found the value of y, we can substitute it back into equation 2 to solve for x:
x + 3(-7) = -24
x - 21 = -24
x = -24 + 21
x = -3
Therefore, the solution to the system of equations is x = -3 and y = -7.