Question

Use the elimination method to solve the systems of equations. Choose the correct ordered pair.

6x + 2y = 8
12x + y = 22

Answer 1

`\huge\boxed{\sf x = 2/3, \ y = 2}`

Explanation:

Given equations:

6x + 2y = 8 -------------(1)

12x + y = 22 ------------(2)

• Multiply Eq. (1) by 2

2(6x + 2y) = 8*2

12x + 4y = 16 -----------(3)

• Subtract Eq. (3) from (2)

12x + 4y - (12x + y) = 16 - 22

12x + 4y - 12x - y = -6

• Cancel 12x

4y - y = 6

3y = 6

• Divide both sides by 3

y = 6/3

y = 2

• Put y = 2 in Eq. (1)

6x + 2(2) = 8

6x + 4 = 8

• Subtract 4 from both sides

6x = 8 - 4

6x = 4

x = 4/6

x = 2/3

`\rule[225]{225}{2}`