a bloody dilemma

if i had a full blood tranfusion one day and the next day commited  a crime but accidently left some of my blood on the scene would forensics be able to determine my DNA ??? ......... i hasten to add that i have no intention of doing anything as mentioned ........ just an errant thought that occured to me.... :)

what's wrong

let x = y be any non-zero number
then multiplying with x throughout gives :
x^2 = xy

and subtracting y^2 gives

x^2 - y^2 = xy - y^2
factorizing both the sides , we get:

(x+y)(x-y) = y(x-y)
x + y = y

2x = y

2 = 1

where is the flaw in the arguments ????