Question

solve the system by substitution.\
\\(-4x + 8y = 40\
\\(-2x = y\\)

Explanation:

Step1: Substitute \( y = -2x \) into the first equation.

We have the first equation \(-4x + 8y = 40\) and the second equation \( y=-2x \). Substitute \( y \) in the first equation with \(-2x\), so we get \(-4x + 8(-2x)=40\).

Step2: Simplify and solve for \( x \).

First, calculate \( 8(-2x)=-16x \), then the equation becomes \(-4x-16x = 40\). Combine like terms: \(-20x = 40\). Divide both sides by \(-20\): \( x=\frac{40}{-20}=-2 \).

Step3: Substitute \( x = -2 \) into \( y=-2x \) to find \( y \).

Substitute \( x=-2 \) into \( y = -2x \), we get \( y=-2\times(-2)=4 \).

Answer:

The solution to the system is \( x = -2 \), \( y = 4 \)