Question

system by substitution.

$3x + 8y = 2$

$y = -2x - 3$

Explanation:

Step1: Substitute \( y = -2x - 3 \) into \( 3x + 8y = 2 \)

We replace \( y \) in the first equation with the expression from the second equation. So we get \( 3x + 8(-2x - 3) = 2 \).

Step2: Simplify the equation

First, distribute the 8: \( 3x - 16x - 24 = 2 \). Then combine like terms: \( -13x - 24 = 2 \).

Step3: Solve for \( x \)

Add 24 to both sides: \( -13x = 2 + 24 \), which simplifies to \( -13x = 26 \). Then divide both sides by -13: \( x = \frac{26}{-13} = -2 \).

Step4: Solve for \( y \)

Substitute \( x = -2 \) into \( y = -2x - 3 \). So \( y = -2(-2) - 3 = 4 - 3 = 1 \).

Answer:

The solution to the system is \( x = -2 \), \( y = 1 \)