Question

How do you solve the following system: `2x-y=7, 2x +5y = 5`?

Answer 1

`(x,y)=(3 1/3, -1/3)`

Explanation:

Given:
[1]`color(white)("XXX")2x-y=7`
[2]`color(white)("XXX")2x+5y=5`

Subtract [2] from[1]
[3]`color(white)("XXX")-6y=2`

Divide both sides by `(-6)` (and reduce the resulting fraction)
[4]`color(white)("XXX")y=-1/3`

Substitute `(-1/3)` for `y` in [1]
[5]`color(white)("XXX")2x-(-1/3)=7`

Subtract `1/3` from both sides
[6]`color(white)("XXX")2x=6 2/3`

Divide both sides by `2`
[7]`color(white)("XXX")x=3 1/3`