AHSME 1960 Problem 18

The pair of equations $3^{x+y}=81$ and $81^{x-y}=3$ has: $\textbf{(A)}\ \text{no common solution} \\ \textbf{(B)}\ \text{the solution} \text{ } x=2, y=2 \\ \textbf{(C)}\ \text{the solution} \text{ } x=2\frac{1}{2}, y=1\frac{1}{2} \\ \textbf{(D)}\text{ a common solution in positive and negative integers} \\ \textbf{(E)}\ \text{none of these}$