I have a "proof" that has an error in it and my goal is to figure out what this error is. The proof:
If $x = y$, then
$$ \begin{eqnarray} x^2 &=& xy \nonumber \\ x^2 - y^2 &=& xy - y^2 \nonumber \\ (x + y)(x - y) &=& y(x-y) \nonumber \\ x + y &=& y \nonumber \\ 2y &=& y \nonumber \\ 2 &=& 1 \end{eqnarray} $$
My best guess is that the error starts with the line $2y = y$. If we accept that $x + y = y$ is true, then
$$ \begin{eqnarray} x + y &=& y \\ x &=& y - y \\ x &=& y = 0 \end{eqnarray} $$
Did I find the error? If not, am I close?