Question

solve the system and write the solution as an ordered pair.
$y = -x + 2$
$3x - 4y = 20$ desmos
$\bigcirc$ $(4, -2)$
$\bigcirc$ $(-2, 4)$
$\bigcirc$ $(4, -1)$
$\bigcirc$ $(4, 2)$

Explanation:

Step1: Substitute \( y = -x + 2 \) into \( 3x - 4y = 20 \)

Substitute \( y \) in the second equation: \( 3x - 4(-x + 2) = 20 \)

Step2: Simplify the equation

Expand and simplify: \( 3x + 4x - 8 = 20 \) → \( 7x - 8 = 20 \)

Step3: Solve for \( x \)

Add 8 to both sides: \( 7x = 28 \) → \( x = 4 \)

Step4: Find \( y \) using \( y = -x + 2 \)

Substitute \( x = 4 \): \( y = -4 + 2 = -2 \)

Answer:

(4, -2)