To solve this system of equations, we can use the method of elimination.
First, let's multiply the first equation by 3 to make the coefficients of y the same as the second equation:
3(6x - 3y) = 3(-6)
18x - 9y = -18
Now, we can subtract the second equation from the equation we just obtained:
(18x - 9y) - (9x - 3y) = (-18) - (-18)
18x - 9y - 9x + 3y = -18 + 18
9x - 6y = 0
Now, let's solve this new equation for x:
9x - 6y = 0
9x = 6y
x = 6y/9
x = 2y/3
Now substitute this value of x into one of the original equations. Let's use the first equation:
6x - 3y = -6
6(2y/3) - 3y = -6
4y - 3y = -6
y = -6
Now substitute this value of y back into the equation we found for x:
x = 2y/3
x = 2(-6)/3
x = -4
Therefore, the solution to the system of equations is x = -4 and y = -6.
6x - 3y = -6
9x - 3y = -18
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