Question

use substitution to solve the system.\\(x = 3y + 19\\)\\(3x - 2y = 22\\)\\(x = \square\\)\\(y = \square\\)

Explanation:

Step1: Substitute \( x = 3y + 19 \) into \( 3x - 2y = 22 \)

We replace \( x \) in the second equation with \( 3y + 19 \). So we get \( 3(3y + 19) - 2y = 22 \).

Step2: Simplify the equation

First, expand the left - hand side: \( 9y+57 - 2y=22 \). Then combine like terms: \( 7y + 57=22 \).

Step3: Solve for \( y \)

Subtract 57 from both sides: \( 7y=22 - 57=-35 \). Then divide both sides by 7: \( y=\frac{-35}{7}=-5 \).

Step4: Solve for \( x \)

Substitute \( y = - 5 \) into \( x = 3y+19 \). So \( x=3\times(-5)+19=-15 + 19 = 4 \).

Answer:

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