Question

use substitution to solve the system.
$5x + 3y = -5$
$y = 2x + 13$
$x = \boxed{}$
$y = \boxed{}$

Explanation:

Step1: Substitute \( y = 2x + 13 \) into \( 5x + 3y = -5 \)

We replace \( y \) in the first equation with \( 2x + 13 \) from the second equation. So we get:
\( 5x + 3(2x + 13) = -5 \)

Step2: Simplify and solve for \( x \)

First, distribute the 3 in \( 3(2x + 13) \):
\( 5x + 6x + 39 = -5 \)
Combine like terms:
\( 11x + 39 = -5 \)
Subtract 39 from both sides:
\( 11x = -5 - 39 \)
\( 11x = -44 \)
Divide both sides by 11:
\( x = \frac{-44}{11} = -4 \)

Step3: Substitute \( x = -4 \) into \( y = 2x + 13 \) to find \( y \)

Plug \( x = -4 \) into the equation for \( y \):
\( y = 2(-4) + 13 \)
\( y = -8 + 13 \)
\( y = 5 \)

Answer:

\( x = -4 \)
\( y = 5 \)