Question

solve using elimination.
-2x + 4y = -20
-4x - y = -13
(□, □)

Explanation:

Step1: Multiply equations to eliminate \( y \)

Multiply the second equation \(-4x - y = -13\) by \( 4 \) to make the coefficients of \( y \) opposites.
New second equation: \( 4\times(-4x - y)=4\times(-13) \)
\( -16x - 4y = -52 \)

Step2: Add the two equations

Add the first equation \(-2x + 4y = -20\) and the new second equation \(-16x - 4y = -52\):
\( (-2x + 4y)+(-16x - 4y)=-20 + (-52) \)
Simplify: \( -18x = -72 \)

Step3: Solve for \( x \)

Divide both sides by \(-18\): \( x=\frac{-72}{-18}=4 \)

Step4: Substitute \( x = 4 \) into an original equation

Use the first equation \(-2x + 4y = -20\). Substitute \( x = 4 \):
\( -2(4)+4y=-20 \)
\( -8 + 4y=-20 \)

Step5: Solve for \( y \)

Add \( 8 \) to both sides: \( 4y=-20 + 8=-12 \)
Divide by \( 4 \): \( y=\frac{-12}{4}=-3 \)

Answer:

\((4, -3)\)