Commutative Property of ... Subtraction?

How many values of x such that there is a value of y that satisfies x-y=y-x, and x≠y?

4 2 3 0 1

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2 solutions

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.

Mahdi Raza
Jun 2, 2020

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

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

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