Use the elimination method to solve the follow system of equations.
9x−7y=22
x+3y=−24
First, let's rearrange the equations so that they are in standard form:
Equation 1: 9x - 7y = 22
Equation 2: x + 3y = -24
Now, multiply both sides of Equation 2 by 7 to make the y-coefficient the same in both equations:
7(x + 3y) = 7(-24)
7x + 21y = -168
Now, we have the system of equations in standard form:
Equation 1: 9x - 7y = 22
Equation 3: 7x + 21y = -168
Now, we can add Equation 1 and Equation 3 to eliminate y:
(9x - 7y) + (7x + 21y) = 22 - 168
16x + 14y = -146
Now, we only have one equation and one variable:
16x + 14y = -146
Now, we can solve for x:
16x = -146 - 14y
16x = -146 - 14(-24)
16x = -146 + 336
16x = 190
x = 190/16
x = 11.875
Now that we have found x, we can substitute it back into either Equation 1 or Equation 2 to find y. Let's use Equation 1:
9(11.875) - 7y = 22
106.875 - 7y = 22
-7y = -84.875
y = 12.125
Therefore, the solution to the system of equations is x = 11.875 and y = 12.125.