Question

use substitution to solve the system.
$x - 3y = -13$
$5x - 3y = -29$
$x = \square$
$y = \square$

Explanation:

Step1: Solve for x from first equation

From \( x - 3y = -13 \), we can express \( x \) as \( x = 3y - 13 \).

Step2: Substitute x into second equation

Substitute \( x = 3y - 13 \) into \( 5x - 3y = -29 \):
\( 5(3y - 13) - 3y = -29 \)
Expand the left side: \( 15y - 65 - 3y = -29 \)
Combine like terms: \( 12y - 65 = -29 \)
Add 65 to both sides: \( 12y = -29 + 65 = 36 \)
Divide both sides by 12: \( y = \frac{36}{12} = 3 \)

Step3: Find x using y

Substitute \( y = 3 \) into \( x = 3y - 13 \):
\( x = 3(3) - 13 = 9 - 13 = -4 \)

Answer:

\( x = -4 \), \( y = 3 \)