Question

olve the system by substitution.

$-x + 2y = -3$
$3y + 4 = x$

Explanation:

Step1: Substitute \( x = 3y + 4 \) into the first equation

We have the first equation \( -x + 2y = -3 \). Replace \( x \) with \( 3y + 4 \):
\( -(3y + 4) + 2y = -3 \)

Step2: Simplify and solve for \( y \)

Expand the left - hand side: \( -3y - 4+2y=-3 \)
Combine like terms: \( -y - 4=-3 \)
Add 4 to both sides: \( -y=-3 + 4=1 \)
Multiply both sides by - 1: \( y=-1 \)

Step3: Substitute \( y = - 1 \) into the equation for \( x \)

We know that \( x = 3y+4 \). Substitute \( y=-1 \):
\( x=3\times(-1)+4=-3 + 4 = 1\)

Answer:

The solution to the system is \( x = 1,y=-1 \)