Question

use the elimination method to solve the system of equations. choose the correct ordered pair. 3x + 6y = 36 3x - 6y = 0 a. (6, 3) b. (3, 6) c. (6, -3) d. (3, -6)

Explanation:

Step1: Eliminate \( y \) by adding equations

Add the two equations \( 3x + 6y = 36 \) and \( 3x - 6y = 0 \) together.
\( (3x + 6y) + (3x - 6y) = 36 + 0 \)
Simplify: \( 6x = 36 \)

Step2: Solve for \( x \)

Divide both sides of \( 6x = 36 \) by 6.
\( x = \frac{36}{6} = 6 \)

Step3: Substitute \( x = 6 \) to find \( y \)

Substitute \( x = 6 \) into the second equation \( 3x - 6y = 0 \).
\( 3(6) - 6y = 0 \)
\( 18 - 6y = 0 \)
Subtract 18 from both sides: \( -6y = -18 \)
Divide by -6: \( y = \frac{-18}{-6} = 3 \)

Answer:

A. \( (6, 3) \)