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

1 Answer
Aug 5, 2015

(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