Question 103732
First, always look at what you've been given
Equation 1: 2x+y+52=2y+50
Equation 2: 2x+y+52=x-3y+131
So, the transitive property tells us:
2y +50 = x -3y + 131
Subtracting 2y from both sides:
50 = x -3y + 2y + 131
Subtracting 50 from both sides:
0 = x -3y + 2y + 131 -50
Combining:
0 = x + y + 81
Subtracting x from both sides:
-x = y + 81
Multiplying by -1:
x = -y -81
Now you can substitute into Eq 1:
2(-y -81) +y +52 = 2y + 50
-2y -162 +y + 52 = 2y + 50
Combining:
-y -110 = 2y + 50
Adding y to both sides:
-110 = 3y + 50
Subtracting 50 from both sides:
-160 = 3y
Dividing through by 3:
-(53+1/3) = y
Since x+y+81=0, then
x+(-(53+1/3))+81=0
x+(27+2/3)=0
Subtract 27 2/3 from both sides
x = -27 2/3
ALWAYS check your work!

x+y=-81
-(27+2/3)+(-(53+1/3))-81 = 0. True

2x+y+52=2y+50
Lefthand side=
2*(-(27+2/3))+(-(53+1/3))+52=-56 2/3
Righthand side=
2(-(53+1/3))+50=-56 2/3
True again.