Question

How do you solve `4x+y=13` and `2x-y=5`?

Answer 1

Add the 2 equations together to get a third equation with the `y` term eliminated; solve for `x`; replace `x` in one of the given equations with the solution to find `y`
`(x,y) = (3,1)`

Explanation:

[1]`color(white)("XXXX")` `4x+y=13`
[2]`color(white)("XXXX")` `2x-y=5`

Add [1] and [2] together
[3]`color(white)("XXXX")` `6x=18`

Divide both sides by `6`
[4]`color(white)("XXXX")` `x=3`

Substitute `3` for `x` in [1]
[5]`color(white)("XXXX")` `4(3)+y=13`

Simplify
[6]`color(white)("XXXX")` `12+y=13`

Subtract `12` from both sides
[7]`color(white)("XXXX")` `y=1`