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 start by simplifying both equations.

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

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

Now we have a new system of equations:
1. \( 2x - y = -2 \)
2. \( 3x - y = -6 \)

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

Now, we can substitute \(x = -4\) back into one of the simplified equations to find \(y\). Let's use the first simplified equation:
\[
2x - y = -2
\]
Substituting \(x\):
\[
2(-4) - y = -2
\]
\[
-8 - y = -2
\]
Adding \(8\) to both sides:
\[
-y = 6
\]
Multiplying both sides by -1:
\[
y = -6
\]

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

Thus, the answer is \((-4, -6)\).