Question

use elimination to solve the system of equations.
$0.3x - 2y = -28$
$0.8x + 2y = 28$
$\left(\square,\square\
ight)$

Explanation:

Step1: Eliminate \( y \) by adding equations

Add the two equations \( 0.3x - 2y = -28 \) and \( 0.8x + 2y = 28 \) together.
\( (0.3x - 2y) + (0.8x + 2y) = -28 + 28 \)
Simplify left side: \( 0.3x + 0.8x - 2y + 2y = 1.1x \)
Simplify right side: \( 0 \)
So, \( 1.1x = 0 \)

Step2: Solve for \( x \)

Divide both sides by \( 1.1 \): \( x = \frac{0}{1.1} = 0 \)

Step3: Substitute \( x = 0 \) into one equation

Use \( 0.8x + 2y = 28 \). Substitute \( x = 0 \):
\( 0.8(0) + 2y = 28 \)
Simplify: \( 2y = 28 \)

Step4: Solve for \( y \)

Divide both sides by \( 2 \): \( y = \frac{28}{2} = 14 \)

Answer:

\( (0, 14) \)