To solve the system of equations:
- \(-6x - 3y = 3\) (Equation 1)
- \(-6x + 3y = 9\) (Equation 2)
We can use either substitution or elimination method. Let's use the elimination method.
First, let's add both equations together:
\[ (-6x - 3y) + (-6x + 3y) = 3 + 9 \]
This simplifies to:
\[ -12x + 0y = 12 \]
So, we have:
\[ -12x = 12 \]
Dividing both sides by -12, we get:
\[ x = -1 \]
Now, we can substitute \(x = -1\) back into one of the original equations to find \(y\). Let's use Equation 1:
\[ -6(-1) - 3y = 3 \]
This simplifies to:
\[ 6 - 3y = 3 \]
Subtracting 6 from both sides gives:
\[ -3y = 3 - 6 \] \[ -3y = -3 \]
Dividing both sides by -3:
\[ y = 1 \]
Thus, the solution to the system of equations is:
\[ x = -1, \quad y = 1 \]
The solution can be written as the ordered pair \((-1, 1)\).