1960 AHSME Problem 18

The pair of equations 3^{x+y}=81 and 81^{x-y}=3 has:

\begin{array}{l} \textbf{(A)}\ \text{no common solution} \qquad \\ \textbf{(B)}\ \text{the solution} \text{ } x=2, y=2\qquad \\ \textbf{(C)}\ \text{the solution} \text{ } x=2\frac{1}{2}, y=1\frac{1}{2} \qquad \\ \textbf{(D)}\text{ a common solution in positive and negative integers} \qquad \\ \textbf{(E)}\ \text{none of these} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.