Question

solve the system of linear equations using the substitution method.
\

$$\begin{cases} x = -5 + 3y \\\\ -4x + 13y = 7 \\end{cases}$$

enter your answer as an ordered pair.

Explanation:

Step1: Substitute \( x = -5 + 3y \) into the second equation

We have the second equation \( -4x + 13y = 7 \). Substitute \( x = -5 + 3y \) into it:
\( -4(-5 + 3y) + 13y = 7 \)

Step2: Simplify and solve for \( y \)

First, distribute the -4:
\( 20 - 12y + 13y = 7 \)
Combine like terms:
\( 20 + y = 7 \)
Subtract 20 from both sides:
\( y = 7 - 20 = -13 \)

Step3: Substitute \( y = -13 \) back into \( x = -5 + 3y \)

\( x = -5 + 3(-13) \)
Calculate \( 3(-13) = -39 \), then:
\( x = -5 - 39 = -44 \)

Answer:

\((-44, -13)\)