Question

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

9x−3y=−18
(1 point)

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. In this case, let's use elimination by subtracting Equation 1 from Equation 2.

First, it is useful to notice that both equations can be simplified.

**Simplifying both equations:**

For Equation 1:
\[
6x - 3y = -6 \quad \text{(Divide by 3)}
\]
\[
2x - y = -2 \quad \text{(Equation 1 simplified)}
\]

For Equation 2:
\[
9x - 3y = -18 \quad \text{(Divide by 3)}
\]
\[
3x - y = -6 \quad \text{(Equation 2 simplified)}
\]

Now we have the simplified system:
1. \( 2x - y = -2 \)
2. \( 3x - y = -6 \)

Now we can eliminate \(y\) by subtracting the first equation from the second:
\[
(3x - y) - (2x - y) = -6 - (-2)
\]
\[
3x - y - 2x + y = -6 + 2
\]
\[
x = -4
\]

Now, substituting \(x = -4\) back into one of the simplified equations to find \(y\). We can use Equation 1:
\[
2(-4) - y = -2
\]
\[
-8 - y = -2
\]
\[
-y = 6
\]
\[
y = -6
\]

Thus, the solution to the system of equations is:
\[
\boxed{(-4, -6)}
\]

To verify, we can substitute \(x = -4\) and \(y = -6\) back into the original equations:

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

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

Thus, the solution \( \boxed{(-4, -6)} \) is correct.