Given
[1]color(white)("XXX")-2y=2x+6XXX−2y=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-4XXX−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-4XXX2x+6=−x−4
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: