Question

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

Explanation:

Step1: Add the two equations to eliminate \(x\)

The two equations are:
\(-7x - 2y = 2\)
\(7x + y = 6\)

Adding them together: \((-7x - 2y)+(7x + y)=2 + 6\)
Simplify the left side: \(-7x+7x-2y + y=-y\)
Simplify the right side: \(8\)
So we get \(-y = 8\), which means \(y=-8\)

Step2: Substitute \(y = -8\) into one of the original equations to find \(x\)

Let's use the second equation \(7x + y = 6\). Substitute \(y=-8\):
\(7x+(-8)=6\)
\(7x - 8 = 6\)
Add 8 to both sides: \(7x=6 + 8\)
\(7x=14\)
Divide both sides by 7: \(x=\frac{14}{7}=2\)

Answer:

\((2, -8)\)