Question

solve the system by substitution.

$-x - 3 = y$
$-3x - 8y = 4$

Explanation:

Step1: Substitute \( y = -x - 3 \) into the second equation

We have the second equation \( -3x - 8y = 4 \). Replace \( y \) with \( -x - 3 \):
\( -3x - 8(-x - 3) = 4 \)

Step2: Simplify the equation

First, distribute the -8:
\( -3x + 8x + 24 = 4 \)
Combine like terms:
\( 5x + 24 = 4 \)

Step3: Solve for \( x \)

Subtract 24 from both sides:
\( 5x = 4 - 24 \)
\( 5x = -20 \)
Divide both sides by 5:
\( x = \frac{-20}{5} = -4 \)

Step4: Find \( y \) using \( y = -x - 3 \)

Substitute \( x = -4 \) into \( y = -x - 3 \):
\( y = -(-4) - 3 = 4 - 3 = 1 \)

Answer:

The solution to the system is \( x = -4 \), \( y = 1 \)