Question

solve using elimination.\
-7x - 2y = 2\
7x + y = 6\
(\square, \square)

Explanation:

Step1: Add the two equations

To eliminate \(x\), we add the equations \(-7x - 2y = 2\) and \(7x + y = 6\) together.
\[

$$\begin{align*} (-7x - 2y)+(7x + y)&=2 + 6\\ -7x - 2y+7x + y&=8\\ - y&=8 \end{align*}$$

\]

Step2: Solve for \(y\)

Multiply both sides by \(- 1\) to solve for \(y\).
\[
y=-8
\]

Step3: Substitute \(y\) into one equation

Substitute \(y = - 8\) into the equation \(7x + y=6\).
\[
7x+(-8)=6
\]

Step4: Solve for \(x\)

First, add \(8\) to both sides of the equation:
\[
7x=6 + 8\\
7x=14
\]
Then, divide both sides by \(7\):
\[
x = 2
\]

Answer:

\((2,-8)\)