Question

How do you solve the system using the elimination method for 2x+y=7 and x+2y=11?

Answer 1

`(x,y) = (1,5)`
`color(white)("XXXX")`(see below for solution by substitution)

Explanation:

[1]`color(white)("XXXX")` `2x+y=7`
[2]`color(white)("XXXX")` `x+2y = 11`

Multiply both sides of [1] by `2` so we have 2 equations with `y` having a coefficient of `2`
[3]`color(white)("XXXX")` `4x+2y=14`

Subtract [2] from [3] eliminating the `y` term
[4]`color(white)("XXXX")` `3x = 3`

Divide both sides by `3`
[5]`color(white)("XXXX")` `x = 1`

Substitute `1` for `x` in [2]
[6]`color(white)("XXXX")` `1+2y=11`
Subtract `1` from both sides
[7]`color(white)("XXXX")` `2y = 10`
Divide both sides by `2`
[8]`color(white)("XXXX")` `y=5`