The Equation 1 = 2

$a = b$
$a^2 = ab$
$a^2 - b^2 = ab - b^2$
$(a - b)(a + b) = b(a - b)$
(a - b)(a + b) = b(a - b)
$(a + b) = b$

$but\ a = b$

$therefore:$

$a + a = a$
$2a = a$

$hence$

$2 = 1$

However, this results in dividing by $0$, because $a - b = a - a = 0$

EDIT:

Your mistake comes in step 5, when you divided by (x-y) on both sides. 
Since x = y, x-y = 0, so you are dividing by zero, which is undefined 
(illegal!). 

Source: http://mathforum.org/library/drmath/view/55792.html