Commutative Property of ... Subtraction?

First we start with the original equation: x-y=y-x

Then we add x to both sides: 2x-y=y

Then we add y to both sides: 2x=2y

Then we divide 2 from both sides: x=y

So the only solution is x=y

But the problem says that x=y is false, so there are 0 possible values of x such that the equation is satisfied.

$\begin{aligned} x-y &= y-x \\ 2x &= 2y \\ x &= y \end{aligned}$

${\color{#D61F06}{\text{But } x \ne y}} \implies \boxed{0}$