Question

use substitution to solve the system.
$x - 3y = -16$
$5x - 3y = -20$
$x = \boxed{}$
$y = \boxed{}$

Explanation:

Step1: Solve for x from first equation

From \( x - 3y = -16 \), we get \( x = 3y - 16 \).

Step2: Substitute x into second equation

Substitute \( x = 3y - 16 \) into \( 5x - 3y = -20 \):
\( 5(3y - 16) - 3y = -20 \)
Expand: \( 15y - 80 - 3y = -20 \)
Simplify: \( 12y - 80 = -20 \)
Add 80 to both sides: \( 12y = 60 \)
Divide by 12: \( y = 5 \).

Step3: Find x using y

Substitute \( y = 5 \) into \( x = 3y - 16 \):
\( x = 3(5) - 16 = 15 - 16 = -1 \).

Answer:

\( x = -1 \), \( y = 5 \)