Question

Solve the system of equations below using the substitution method. x = y + 7 / 2 4x − 2y = 8

Answer 1

y = -3

x =
`(1)/(2)`

Explanation:

4(y +
`(7)/(2)`) - 2y = 8 Distribute the 4. Multiply everything in the parentheses by 4

4y + 14 - 2y = 8 4
`((7)/(2))` =
`(28)/(2)` = 14 Combine the like terms 4y and -2y

2y + 14 = 8 Subtract 14 from both sides

2y = -6 Divide both sides by 2

y = -3

Plug -3 in for y in either original equation.

4x - 2y = 8

4x -2(-3) = 8

4x + 6 = 8 Subtract 6 from both sides

4x = 2 Divide both sides by 4

x =
`(2)/(4)` =
`(1)/(2)`

Check:

x = y +
`(7)/(2)`

`(1)/(2)` = -3+
`(7)/(2)`

`(1)/(2)` =
`(-6)/(2)` +
`(7)/(2)`

`(1)/(2)` =
`(1)/(2)`

4x - 2y = 8

4(
`(1)/(2)`) - 2(-3) = 8

2 + 6 = 8

8 = 8