How do you solve the following system?: -2y=2x+6 , y= 1/2x +2 2y=2x+6,y=12x+2

1 Answer
May 13, 2017

(x,y)=(-3 1/3, 1/3)(x,y)=(313,13)

Explanation:

Given
[1]color(white)("XXX")-2y=2x+6XXX2y=2x+6
[2]color(white)("XXX")y=1/2x+2XXXy=12x+2

Multiplying both sides of [2] by (-2)(2)
[3]color(white)("XXX")-2y=-x-4XXX2y=x4

Since the left sides of [1] and [3] are equal
the right sides must also be equal
[4]color(white)("XXX")2x+6=-x-4XXX2x+6=x4

Adding xx to both sides of [4]
[5]color(white)("XXX")3x+6=-4XXX3x+6=4

Subtracting 66 from both sides of [5]
[6]color(white)("XXX")3x=-10XXX3x=10

Dividing both sides of [6] by 33
[7]color(white)("XXX")x=-10/3 (=-3 1/3)XXXx=103(=313)

Substituting (-10/3)(103) for xx in [2]
[8]color(white)("XXX")y=1/2xx(-10/3)+2XXXy=12×(103)+2

color(white)("XXXXX")=-5/3+2XXXXX=53+2

color(white)("XXXXX")=1/3XXXXX=13

(x,y)=(-10/3,1/3)(x,y)=(103,13)

The graphic solution (below) supports this result:
enter image source here