2 = 1

If x = 1 and y = 1 then:

x = y

1. Multiplying each side by x gives:

x² = xy

2. Subtracting y² from each side gives:

x²-y² = xy-y²

3. Factoring each side gives:

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

4. Dividing out the common term (x-y) gives:

x+y = y

5. When we put the initial values back in place we get:

1+1 = 1 or
2 = 1

What's wrong with the proof?