To solve the system of equations:
- \(6x - 3y = -6\) (Equation 1)
- \(9x - 3y = -18\) (Equation 2)
We can start by rewriting both equations to see if they are equivalent or have a unique solution.
Let's simplify each equation.
From Equation 1: \[ 6x - 3y = -6 \] Divide the entire equation by 3: \[ 2x - y = -2 \quad \text{(Equation 1 simplified)} \]
From Equation 2: \[ 9x - 3y = -18 \] Divide the entire equation by 3: \[ 3x - y = -6 \quad \text{(Equation 2 simplified)} \]
Now, we can compare the two simplified equations:
- \(2x - y = -2\)
- \(3x - y = -6\)
Next, let's use the method of elimination. Subtract Equation 1 from Equation 2:
\[ (3x - y) - (2x - y) = -6 - (-2) \] This simplifies to: \[ 3x - 2x = -6 + 2 \] Which gives: \[ x = -4 \]
Now, substitute \(x = -4\) back into one of the original equations to find \(y\). We'll use Equation 1:
\[ 6(-4) - 3y = -6 \] This simplifies to: \[ -24 - 3y = -6 \] Adding 24 to both sides: \[ -3y = 18 \] Dividing by -3: \[ y = -6 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-4, -6) \]
The final answer is: \[ \boxed{(-4, -6)} \]