Question

Solve the system of equations.
6x−3y=−6

9x−3y=−18
(1 point)
(
,
)

Answer 1

To solve the system of equations:

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

We can start by manipulating the equations.

First, let's express each equation in a simpler form by dividing all terms in each equation by the coefficients of \( y \).

1. Divide the first equation by 3:
\[
2x - y = -2 \quad \text{(Equation 1)}
\]

2. Divide the second equation by 3:
\[
3x - y = -6 \quad \text{(Equation 2)}
\]

Now we have the following simplified system of equations:

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

Now let's subtract Equation 1 from Equation 2:

\[
(3x - y) - (2x - y) = -6 - (-2)
\]
\[
3x - y - 2x + y = -6 + 2
\]
\[
x = -4
\]

Now that we have the value of \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use Equation 1:

\[
2(-4) - y = -2
\]
\[
-8 - y = -2
\]
\[
-y = -2 + 8
\]
\[
-y = 6
\]
\[
y = -6
\]

So, the solution to the system of equations is:

\[
(x, y) = (-4, -6)
\]

Hence, the final answer is:

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