Question

How do you solve `x+2y=1` and `3x-4y=1`?

Answer 1

`(x,y) = (2/5,1/5)`

Explanation:

[1]`color(white)("XXX")x+2y=1`
[2]`color(white)("XXX")3x-4y=1`

Multiply [1] by `2`
[3]`color(white)("XXX")2x+4y=2`

Add [2] and [3]
[4]`color(white)("XXX")5x=3`

Divide [4] by `5`
[5]`color(white)("XXX")x=3/5`

Substitute `3/5` for `x` in [1]
[6]`color(white)("XXX")3/5+2y=1`

Subtract `3/5` from both sides of [6]
[7]`color(white)("XXX")2y = 2/5`

Divide [7] by `2`
[8]`color(white)("XXX")y=1/5`