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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