Question

solve using elimination.
2x - 3y = -13
-2x + 2y = 4
(□, □)

Explanation:

Step1: Add the two equations

Add the equations \(2x - 3y = -13\) and \(-2x + 2y = 4\) together.
\((2x - 3y)+(-2x + 2y)=-13 + 4\)
Simplify the left - hand side: \(2x-2x-3y + 2y=-y\), and the right - hand side: \(-9\). So we get \(-y=-9\).

Step2: Solve for y

Multiply both sides of the equation \(-y = -9\) by \(- 1\) to solve for \(y\). We have \(y = 9\).

Step3: Substitute y into one of the original equations

Substitute \(y = 9\) into the second equation \(-2x+2y = 4\). So \(-2x+2\times9=4\).
Simplify the left - hand side: \(-2x + 18=4\).
Subtract 18 from both sides: \(-2x=4 - 18=-14\).
Divide both sides by \(-2\): \(x=\frac{-14}{-2}=7\).

Answer:

\((7,9)\)