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

1 Answer
Alan P.
May 13, 2017

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

Explanation:

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

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

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

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

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

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

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

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

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

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

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

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