Use the elimination method to solve the following system of equations
9x - 7y = 22
x + 3y = -24
To use the elimination method, we want to add the two equations together in a way that eliminates one of the variables. Let's start by multiplying the second equation by 7 to make the coefficients of y in both equations the same.
Original equations:
1) 9x - 7y = 22
2) x + 3y = -24
1) 9x - 7y = 22
7 * 2) 7x + 21y = -168
Now we can add these two equations together:
9x - 7y + 7x + 21y = 22 - 168
16x + 14y = -146
Next, we can divide the entire equation by 2 to simplify the coefficients:
8x + 7y = -73
So, the new equation we obtained is:
8x + 7y = -73
Let's add this new equation to the original equation 1) to eliminate y:
9x - 7y + 8x + 7y = 22 - 73
17x = -51
Dividing by 17 on both sides, we get:
x = -3
Now that we have the value of x, we can substitute it back into the original second equation to solve for y:
x + 3y = -24
-3 + 3y = -24
3y = -21
y = -7
Therefore, the solution to the system of equations is x = -3 and y = -7.