Question

solve the system by substitution.
$y = -5x - 40$
$y = 5x$

Explanation:

Step1: Substitute \( y = 5x \) into \( y = -5x - 40 \)

Since both equations are solved for \( y \), we can set them equal to each other. So we substitute \( 5x \) for \( y \) in the first equation: \( 5x = -5x - 40 \)

Step2: Solve for \( x \)

Add \( 5x \) to both sides of the equation: \( 5x + 5x = -5x - 40 + 5x \), which simplifies to \( 10x = -40 \). Then divide both sides by 10: \( x=\frac{-40}{10}=-4 \)

Step3: Solve for \( y \)

Substitute \( x = -4 \) into \( y = 5x \): \( y = 5\times(-4)=-20 \)

Answer:

The solution to the system is \( x = -4 \) and \( y = -20 \), or as an ordered pair \( (-4, -20) \)