Question

graphs and functions
solving a system of linear equations using substitution
use substitution to solve the system.
$y = 2x - 8$
$5x - 2y = 18$
$x = \square$
$y = \square$

Explanation:

Step1: Substitute \( y = 2x - 8 \) into \( 5x - 2y = 18 \)

Substitute \( y \) in the second equation: \( 5x - 2(2x - 8) = 18 \)

Step2: Simplify the equation

Expand and simplify: \( 5x - 4x + 16 = 18 \) → \( x + 16 = 18 \)

Step3: Solve for \( x \)

Subtract 16 from both sides: \( x = 18 - 16 = 2 \)

Step4: Solve for \( y \)

Substitute \( x = 2 \) into \( y = 2x - 8 \): \( y = 2(2) - 8 = 4 - 8 = -4 \)

Answer:

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