Question

solve using elimination.
-6x + 4y = -12
5x - 4y = 16
(\square, \square)

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \(-6x + 4y=-12\) and \(5x - 4y = 16\) together.
\[

$$\begin{align*} (-6x + 4y)+(5x - 4y)&=-12 + 16\\ -6x+4y + 5x-4y&=4\\ (-6x+5x)+(4y - 4y)&=4\\ -x&=4 \end{align*}$$

\]

Step2: Solve for \( x \)

Multiply both sides of \(-x = 4\) by \(- 1\) to solve for \( x \).
\[
x=-4
\]

Step3: Substitute \( x \) into one equation

Substitute \( x=-4 \) into the first equation \(-6x + 4y=-12\).
\[

$$\begin{align*} -6(-4)+4y&=-12\\ 24 + 4y&=-12 \end{align*}$$

\]

Step4: Solve for \( y \)

Subtract 24 from both sides:
\[
4y=-12 - 24\\
4y=-36
\]
Divide both sides by 4:
\[
y=\frac{-36}{4}=-9
\]

Answer:

\((-4, -9)\)