Question

elimination with addition and subtraction
question 6 of 15 (1 point) | question attempt: 1 of 3

solve the following system of equations.
$5x + 2y = -4$
$3x - 2y = 20$

$x = \square$
$y = \square$

Explanation:

Step1: Eliminate \( y \) by adding equations

Add the two equations \( 5x + 2y = -4 \) and \( 3x - 2y = 20 \) together.
\( (5x + 2y) + (3x - 2y) = -4 + 20 \)
Simplify: \( 5x + 3x + 2y - 2y = 16 \) → \( 8x = 16 \)

Step2: Solve for \( x \)

Divide both sides of \( 8x = 16 \) by 8.
\( x = \frac{16}{8} = 2 \)

Step3: Substitute \( x = 2 \) into one equation

Substitute \( x = 2 \) into \( 5x + 2y = -4 \).
\( 5(2) + 2y = -4 \) → \( 10 + 2y = -4 \)

Step4: Solve for \( y \)

Subtract 10 from both sides: \( 2y = -4 - 10 = -14 \)
Divide by 2: \( y = \frac{-14}{2} = -7 \)

Answer:

\( x = 2 \), \( y = -7 \)