Question

Solve the system of equations 6x-3y=-6 and 9x-3y=-18

Answer 1

To solve the system of equations:

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

We can solve for \( y \) by eliminating one of the variables. First, we can subtract the first equation from the second equation:

\[
(9x - 3y) - (6x - 3y) = -18 - (-6)
\]

This simplifies to:

\[
9x - 6x - 3y + 3y = -18 + 6
\]

Which further simplifies to:

\[
3x = -12
\]

Dividing both sides by 3 gives:

\[
x = -4
\]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). We will use the first equation:

\[
6(-4) - 3y = -6
\]

This simplifies to:

\[
-24 - 3y = -6
\]

Adding 24 to both sides gives:

\[
-3y = 18
\]

Dividing both sides by -3 gives:

\[
y = -6
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-4, -6)}
\]

To verify, we can check that these values satisfy both original equations:

For \( 6x - 3y = -6 \):
\[
6(-4) - 3(-6) = -24 + 18 = -6 \quad \text{(True)}
\]

For \( 9x - 3y = -18 \):
\[
9(-4) - 3(-6) = -36 + 18 = -18 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution is indeed \( \boxed{(-4, -6)} \).