Question

use substitution to solve the system. 2x + 5y = -2; x = 2y + 8

Explanation:

Step1: Substitute \( x = 2y + 8 \) into \( 2x + 5y = -2 \)

Substitute \( x \) in the first equation: \( 2(2y + 8) + 5y = -2 \)

Step2: Simplify and solve for \( y \)

Expand: \( 4y + 16 + 5y = -2 \)
Combine like terms: \( 9y + 16 = -2 \)
Subtract 16: \( 9y = -2 - 16 = -18 \)
Divide by 9: \( y = \frac{-18}{9} = -2 \)

Step3: Substitute \( y = -2 \) into \( x = 2y + 8 \)

Calculate \( x \): \( x = 2(-2) + 8 = -4 + 8 = 4 \)

Answer:

\( x = 4 \), \( y = -2 \)