Question

How do you solve the following system: `3x - 2y = 9, 2x + 3y = 34`?

Answer 1

`(x,y)= (95/13, 84/13)`

Explanation:

Given:
[1]`color(white)("XXX")3x-2y=9`
[2]`color(white)("XXX")2x+3y=34`

Multiply [1] by 3 and [2] by 2 to get equivalent coefficients for `y`
[3]`color(white)("XXX")9x-6y=27`
[4]`color(white)("XXX")6x+6y=68`

Add [3] and [4]
[5]`color(white)("XXX")13x= 95`

Divide both sides by 13
[6]`color(white)("XXX")x=95/13`

Substitute `13` for `x` in [1]
[7]`color(white)("XXX")3*(95/13)-2y=9`

Simplify
[8]`color(white)("XXX")2y= 285/13-9 = (285-117)/13 = 168/13`

[9]`color(white)("XXX")y=84/13`