x-y=x+y+17

First we solve the equation for y

$$\begin{array}{lcl}
x - y = x + y + 17\\
-y = y + 17\\
-2y = 17\\
y = -\frac{17}{2}
\end{array}$$

We have 2 possible situations for x

either 

$$\begin{array}{lcl}
y = -\frac{17}{2}\\
\end{array}$$

and we find

$$\begin{array}{lcl}
x - y = x + y + 17\\
x + \frac{17}{2} = x - \frac{17}{2} + 17\\
x = x - 17 + 17\\
x = x
\end{array}$$

Which means x can be any number,

or

$$\begin{array}{lcl}
y \neq -\frac{17}{2}\\
\end{array}$$

and we find no value for x for which the equation holds.

 

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