Question

How do you solve the system of equations `2x - y = 2` and `3x + y = 13`?

Answer 1

(x,y)=(3,4)

Explanation:

Given
[1]`color(white)("XXX")2x-y=2`
[2]`color(white)("XXX")3x+y=13`

By adding the 2 equations together we can eliminate the `y` term
[3]`color(white)("XXX")5x=15`

Dividing both sides by `5`
[4]`color(white)("XXX")x=3`

We can now substitute `3` for `x` in either [1] or [2]
(I've chosen [1] for this example)
[5]`color(white)("XXX")2*(3)-y=2`

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

Add `y` to both sides and subtract `2` from both sides
[7]`color(white)("XXX")4=ycolor(white)("XXX")"or " y=4`