Question

solve the system by substitution.

$y = 5x - 24$
$y = -3x$

Explanation:

Step1: Substitute \( y = -3x \) into \( y = 5x - 24 \)

Since both equations are solved for \( y \), we can set them equal to each other. So substitute \( y \) in the first equation with \( -3x \) from the second equation: \( -3x = 5x - 24 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( -3x - 5x = 5x - 24 - 5x \) which simplifies to \( -8x = -24 \). Then divide both sides by \( -8 \): \( x=\frac{-24}{-8}=3 \)

Step3: Solve for \( y \)

Substitute \( x = 3 \) into \( y = -3x \): \( y=-3\times3=-9 \)

Answer:

The solution to the system is \( x = 3 \) and \( y = -9 \), or as an ordered pair \( (3, -9) \)