Question

How do you solve using elimination of `x+y=10` and `x-y=2`?

Answer 1

By adding the two equations together you eliminate the `y` variable which allows you to solve `x=6`.
Alternately, subtract one equation form the other eliminating the `x` and allowing `y=4`

Explanation:

Given
[1]`color(white)("XXX")x+y=10`
[2]`color(white)("XXX")x-y=2`

Add [1] and [2]
[3]`color(white)("XXX")2x=12`
`rarr`[4]`color(white)("XXX")x=6`

Subtract [2] from [1]
[5]`color(white)("XXX")2y=8`
`rarr` `color(white)("XXX")y=4`