x = 5 and y = 7
x+1/2 = x+y/4 ...................... (1)
y+2/3 = x+y/4 ..................... (2)
From (1):
x+1/2 = x+y/4
4(x+1) = 2(x+y)
4x + 4 = 2x + 2y
4 = 2x + 2y - 4x
4 = -2x + 2y
2x - 2y = -4
2(x - y) = -4
x - y = -4/2
x - y = -2
x = y - 2 .................... (3)
From (2):
y+2/3 = x+y/4
4(y+2) = 3(x+y)
4y + 8 = 3x + 3y
4y - 3x - 3y = -8
-3x + y = -8 .................... (4)
Sub (3) into (4):
-3(y-2) + y = -8
-3y + 6 + y = -8
-2y = -8 - 6
-2y = -14
y = 7
Sub y = 7 into (3):
x = (7) - 2
x = 5
