AHSME 1968 Problem 14

If $x$ and $y$ are non-zero numbers such that $x=1+\frac{1}{y}$ and $y=1+\frac{1}{x}$, then $y$ equals $\text{(A) } x-1 \text{(B) } 1-x \text{(C) } 1+x \text{(D) } -x \text{(E) } x$