To solve the system of equations:
- \(-x - 3y = -3\)
- \(x - 6y = -24\)
We can start by rewriting these equations in a more standard format.
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\(-x - 3y = -3\) can be rewritten as: \[ x + 3y = 3 \quad \text{(by multiplying the entire equation by -1)} \]
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The second equation remains the same: \[ x - 6y = -24 \]
Now we have the system:
- \(x + 3y = 3\)
- \(x - 6y = -24\)
Next, we can solve this system using the substitution or elimination method. Here we'll use the elimination method.
We can eliminate \(x\) by subtracting the first equation from the second one. Let’s rewrite both equations for clarity:
\[ \begin{align*} (1) & \quad x + 3y = 3 \quad \text{(Equation 1)} \ (2) & \quad x - 6y = -24 \quad \text{(Equation 2)} \end{align*} \]
Subtract Equation 1 from Equation 2: \[ (x - 6y) - (x + 3y) = -24 - 3 \]
This simplifies to: \[ -6y - 3y = -27 \] \[ -9y = -27 \]
Dividing both sides by -9: \[ y = 3 \]
Now that we have the value for \(y\), we can substitute it back into either of the original equations to find \(x\). Let's use the first equation:
\[ x + 3(3) = 3 \] \[ x + 9 = 3 \] Subtract 9 from both sides: \[ x = 3 - 9 \] \[ x = -6 \]
So, the solution to the system of equations is: \[ \boxed{(-6, 3)} \]
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