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

1 Answer
Aug 5, 2015

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

Explanation:

[1]color(white)("XXXX")XXXXx+2y=3x+2y=3
[2]color(white)("XXXX")XXXX3x-y=-53xy=5

Multiply [2] by 2 (so the coefficient of yy corresponds to that in [1])
[3]color(white)("XXXX")XXXX6x-2y=-106x2y=10

Add [1] and [3] (eliminating the yy term)
[4]color(white)("XXXX")XXXX7x = -77x=7

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

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

Add 1 to both sides of [6]
[7]color(white)("XXXX")XXXX2y=42y=4

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