Question

Systems of Linear Equations Unit Test
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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. \(4x + 3y = -9\)

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

First, we can simplify the first equation. Divide the entire equation by 2:

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

Now we can rewrite the system of equations:

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

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

\[
y = 3x - 16
\]

Now, substitute \(y\) in the second equation:

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

Distributing:

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

Combine like terms:

\[
13x - 48 = -9
\]

Add 48 to both sides:

\[
13x = 39
\]

Divide by 13:

\[
x = 3
\]

Now, substitute \(x = 3\) back into the equation for \(y\):

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

So, the solution to the system of equations is:

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