Question

How do you solve the system `x+y=7` and `2x-y=2` by addition?

Answer 1

`(x,y)=(3,4)`

Explanation:

Given
`color(white)("XXX")color(red)(x+y)=color(red)(7)`
`color(white)("XXX")color(blue)(2x-y)=color(blue)(2)`

Adding the two equations together
`color(white)("XXX")color(red)(x)+color(blue)(2x)+color(red)(y)+color(blue)((-y))=color(red)(7)+color(blue)(2)`

`color(white)("XXX")3x = 9`

`color(white)("XXX")x=3`

The we can substitute `3` for `x` in `color(blue)(2x-y=2)`
to get
`color(white)("XXX")2(3)-y=2`

`color(white)("XXX")6-y=2`

`color(white)("XXX")y=4`