Question

1. use substitution to solve this system of equations. show all of your work and write your solution as an ordered pair.

( x + 3y = -2 )
( y = -5x - 24 )

Explanation:

Step1: Substitute \( y = -5x - 24 \) into \( x + 3y = -2 \)

We know \( y = -5x - 24 \), so replace \( y \) in the first equation with this expression. The first equation is \( x + 3y = -2 \), substituting gives \( x + 3(-5x - 24) = -2 \).

Step2: Simplify and solve for \( x \)

First, expand the left - hand side: \( x-15x - 72=-2 \). Combine like terms: \( -14x-72 = - 2 \). Add 72 to both sides: \( -14x=-2 + 72=70 \). Then divide both sides by - 14: \( x=\frac{70}{-14}=-5 \).

Step3: Substitute \( x = - 5 \) into \( y=-5x - 24 \) to find \( y \)

Substitute \( x=-5 \) into \( y=-5x - 24 \), we get \( y=-5\times(-5)-24=25 - 24 = 1 \).

Answer:

The solution as an ordered pair is \((-5,1)\)