Question

solve the system by substitution.
y = -8x - 24
y = -4x

Explanation:

Step1: Substitute \( y = -4x \) into \( y = -8x - 24 \)

Since both equations are solved for \( y \), we can set them equal to each other. So substitute \( -4x \) for \( y \) in the first equation: \( -4x = -8x - 24 \)

Step2: Solve for \( x \)

Add \( 8x \) to both sides of the equation: \( -4x + 8x = -8x - 24 + 8x \)
Simplify both sides: \( 4x = -24 \)
Divide both sides by 4: \( \frac{4x}{4} = \frac{-24}{4} \)
Which gives \( x = -6 \)

Step3: Find \( y \) by substituting \( x = -6 \) into \( y = -4x \)

Substitute \( x = -6 \) into \( y = -4x \): \( y = -4\times(-6) \)
Calculate the right side: \( y = 24 \)

Answer:

The solution to the system is \( x = -6 \) and \( y = 24 \), or as an ordered pair \( (-6, 24) \)