Question

solve the system by substitution.

$x = -y + 2$
$4x - 6y = -22$

Explanation:

Step1: Substitute \( x = -y + 2 \) into \( 4x - 6y = -22 \)

We replace \( x \) in the second equation with \( -y + 2 \) from the first equation. So we get \( 4(-y + 2) - 6y = -22 \).

Step2: Simplify the equation

First, distribute the 4 in \( 4(-y + 2) \): \( -4y + 8 - 6y = -22 \). Then combine like terms: \( -10y + 8 = -22 \).

Step3: Solve for \( y \)

Subtract 8 from both sides: \( -10y = -22 - 8 = -30 \). Then divide both sides by -10: \( y = \frac{-30}{-10} = 3 \).

Step4: Solve for \( x \)

Substitute \( y = 3 \) into the first equation \( x = -y + 2 \): \( x = -3 + 2 = -1 \).

Answer:

The solution to the system is \( x = -1 \), \( y = 3 \)