Question

Solve the system of equations.
−6x+2y=−32

4x+3y=−9
(1 point)

Answer 1

To solve the system of equations:

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

Let's first simplify the first equation. We can divide the entire equation by 2:

\[
-3x + y = -16
\]

Now we can rewrite it in terms of \(y\):

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

Next, we can substitute this expression for \(y\) into the second equation:

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

Now, simplify the equation:

\[
4x + 9x - 48 = -9
\]
\[
13x - 48 = -9
\]

Adding 48 to both sides:

\[
13x = 39
\]

Now, divide by 13:

\[
x = 3
\]

Now that we have \(x\), we can substitute it back into Equation 1 to find \(y\):

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

Thus, the solution to the system of equations is:

\[
\boxed{(3, -7)}
\]