Question

Solve the system of equations.
−6x+2y=−32
4x+3y=−9 (1 point)
(, )

Answer 1

To solve the system of equations:

1. **Equation 1:** \(-6x + 2y = -32\)
2. **Equation 2:** \(4x + 3y = -9\)

We can use the substitution or elimination method. Here, I'll use the elimination method.

First, let's rewrite the first equation in a simpler form. Divide the entire equation by 2:

\[
-3x + y = -16 \quad \text{(Equation 1 simplified)}
\]

Now we have:

1. \( -3x + y = -16 \)
2. \( 4x + 3y = -9 \)

Next, we can express \(y\) from the first equation:

\[
y = 3x - 16
\]

Now substitute this expression for \(y\) into the second equation:

\[
4x + 3(3x - 16) = -9
\]

Distributing:

\[
4x + 9x - 48 = -9
\]

Combine like terms:

\[
13x - 48 = -9
\]

Add 48 to both sides:

\[
13x = 39
\]

Now, divide by 13:

\[
x = 3
\]

Now that we have \(x\), we can substitute it back into the equation for \(y\):

\[
y = 3(3) - 16
\]
\[
y = 9 - 16
\]
\[
y = -7
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (3, -7)
\]

So the answer is \((3, -7)\).