To solve the system of equations:
- \(6x - 3y = -6\) (Equation 1)
- \(9x - 3y = -18\) (Equation 2)
First, notice that both equations have a common term, \(-3y\). Let's try to eliminate \(y\) by subtracting the first equation from the second:
\[ (9x - 3y) - (6x - 3y) = -18 - (-6) \]
This simplifies to:
\[ 9x - 3y - 6x + 3y = -18 + 6 \]
Combining like terms, we have:
\[ 3x = -12 \]
Now, divide both sides by 3:
\[ x = -4 \]
Now that we have \(x\), we can substitute it back into either equation to find \(y\). Let's use Equation 1:
\[ 6(-4) - 3y = -6 \]
This simplifies to:
\[ -24 - 3y = -6 \]
Next, add 24 to both sides:
\[ -3y = 18 \]
Now, divide by -3:
\[ y = -6 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, -6) \]
So the final answer is:
\[ \boxed{(-4, -6)} \]