Question

use substitution to solve the system.
3x + 2y = 19
x - 3y = -12
x =

y =

Explanation:

Step1: Solve for x from the second equation

From \( x - 3y = -12 \), we can express \( x \) as \( x = 3y - 12 \).

Step2: Substitute x into the first equation

Substitute \( x = 3y - 12 \) into \( 3x + 2y = 19 \):
\( 3(3y - 12) + 2y = 19 \)
Expand the left side: \( 9y - 36 + 2y = 19 \)
Combine like terms: \( 11y - 36 = 19 \)
Add 36 to both sides: \( 11y = 19 + 36 = 55 \)
Divide both sides by 11: \( y = \frac{55}{11} = 5 \)

Step3: Solve for x using y = 5

Substitute \( y = 5 \) into \( x = 3y - 12 \):
\( x = 3(5) - 12 = 15 - 12 = 3 \)

Answer:

\( x = 3 \), \( y = 5 \)