2x-3y+2=x+2y-5=3x+y

2x-3y+2=x+2y-5 subtract right from left

is
x - 5 y + 7 = 0

x+2y-5=3x+y subtract again
-2 x + y - 5 = 0
so y = 2 x + 5, substitute that in the top one

x - 5(2x+5) + 7 = 0
-9 x- 18 =0
x = -2
then y = -4+5 = 1
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check
2x-3y+2=x+2y-5
-4- 3 + 2 = -2 + 2 -5
-5 = -5 wheww !!!