Question

solve the system by substitution.

$-3x - 10 = y$

$-x - 8y = 11$

Explanation:

Step1: Substitute \( y = -3x - 10 \) into the second equation

We have the second equation \( -x - 8y = 11 \). Substitute \( y \) with \( -3x - 10 \), so we get \( -x - 8(-3x - 10) = 11 \).

Step2: Simplify the equation

First, distribute the -8: \( -x + 24x + 80 = 11 \). Then combine like terms: \( 23x + 80 = 11 \).

Step3: Solve for \( x \)

Subtract 80 from both sides: \( 23x = 11 - 80 \), so \( 23x = -69 \). Then divide both sides by 23: \( x = \frac{-69}{23} = -3 \).

Step4: Solve for \( y \)

Substitute \( x = -3 \) into \( y = -3x - 10 \). So \( y = -3(-3) - 10 = 9 - 10 = -1 \).

Answer:

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