Solve the system of equations 6x - 3y = -6 9x - 3y = -18
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.
First, let's multiply the second equation by 2 to make the coefficients of y the same in both equations:
2(9x - 3y) = 2(-18)
18x - 6y = -36
Now, we can subtract the first equation from this equation:
(18x - 6y) - (6x - 3y) = (-36) - (-6)
18x - 6y - 6x + 3y = -36 + 6
12x - 3y = -30
Now, we have a new equation: 12x - 3y = -30
Next, we can rearrange this equation to solve for x:
12x = 3y - 30
x = (3y - 30)/12
x = (y - 10)/4
Now, we can substitute this expression for x into the first equation:
6[(y - 10)/4] - 3y = -6
Multiply both sides by 4 to eliminate the fraction:
6(y - 10) - 12y = -24
6y - 60 - 12y = -24
-6y - 60 = -24
-6y = 36
y = -6
Now, substitute this value of y back into the expression for x:
x = (y - 10)/4
x = (-6 - 10)/4
x = -16/4
x = -4
Therefore, the solution to the system of equations is x = -4 and y = -6.