Question

How do you solve the system of equations: x+2y=3, 3x-y= -5?

Answer 1

`(x,y) = (-1,2)`

Explanation:

[1]`color(white)("XXXX")` `x+2y=3`
[2]`color(white)("XXXX")` `3x-y=-5`

Multiply [2] by 2 (so the coefficient of `y` corresponds to that in [1])
[3]`color(white)("XXXX")` `6x-2y=-10`

Add [1] and [3] (eliminating the `y` term)
[4]`color(white)("XXXX")` `7x = -7`

Divide [4] by 7
[5]`color(white)("XXXX")` `x = -1`

Substitute `(-1)` for `x` in [1]
[6]`color(white)("XXXX")` `(-1)+2y = 3`

Add 1 to both sides of [6]
[7]`color(white)("XXXX")` `2y=4`

Divide both sides by 2
[8]`color(white)("XXXX")` `y=2`