Question

A system of equations is shown below.

Equation 1: 2x−y=−8
Equation 2: x+2y=6
To begin solving the system of equations, Equation 1 is multiplied by a value of 2 to create Equation 3.

Equation 3: 4x−2y=−16
Equation 2: x+2y=6
Which procedure could best be used to eliminate one of the variables?

Possible Answers:
add Equation 2 to Equation 3

subtract Equation 2 from Equation 3

subtract Equation 3 from Equation 2

multiply Equation 2 by a value of 4

Answer 1

add equation 2 to equation 3

Explanation:

x + 2y = 6 → (2)

4x - 2y = - 16 → (3)

adding (2) and (3) term by term will eliminate y

5x + 0 = - 10

5x = - 10 ( divide both sides by 5 )

x = - 2

substitute x = - 2 into either equation (1) or equation(2) and solve for y

substituting into (2)

- 2 + 2y = 6 ( add 2 to both sides )

2y = 8 ( divide both sides by 2 )

y = 4

solution is x = - 2 and y = 4