3. If the system of equations
$$
\begin{array}{l}
|x+y|=99 \\
|x-y|=c
\end{array}
$$
has exactly two real solutions $(x, y)$, find the value of $c$.
Solution:
0

If $c0$ then we have four possible systems of linear equations given by $x+y= \pm 99, x-y= \pm c$, giving four solutions $(x, y)$. So we must have $c=0$, and then we do get two solutions $(x=y$, so they must both equal $\pm 99 / 2)$.