Question

6x−3y=−6

9x−3y=−18

Answer 1

To solve the system of equations:

1. \( 6x - 3y = -6 \) (Equation 1)
2. \( 9x - 3y = -18 \) (Equation 2)

We can start by observing that both equations can be simplified.

### Simplifying Equation 1:
\[
6x - 3y = -6
\]
Divide the entire equation by 3:
\[
2x - y = -2 \quad \text{(Equation 1 simplified)}
\]

### Simplifying Equation 2:
\[
9x - 3y = -18
\]
Divide the entire equation by 3:
\[
3x - y = -6 \quad \text{(Equation 2 simplified)}
\]

Now, we have a new system of equations:

1. \( 2x - y = -2 \) (Equation 1 simplified)
2. \( 3x - y = -6 \) (Equation 2 simplified)

### Solving the System:
Now we can set the two simplified equations equal to each other since they both equal \(y\):
\[
2x + 2 = 3x + 6
\]

Rearranging gives us:
\[
2 = 3x - 2x + 6
\]
\[
2 = x + 6
\]
Subtracting 6 from both sides, we find:
\[
x = -4
\]

Now we can substitute \(x = -4\) back into one of the simplified equations to find \(y\). We'll use Equation 1 simplified:
\[
2(-4) - y = -2
\]
\[
-8 - y = -2
\]
Adding 8 to both sides:
\[
-y = 6
\]
Multiplying by -1 gives us:
\[
y = -6
\]

### Solution:
The solution to the system of equations is:
\[
(x, y) = (-4, -6)
\]