1.23 If $x, y$ are non-zero real numbers satisfying $x=1+\frac{1}{y}$ and $y=1+\frac{1}{x}$, then $y$ equals
(A) $x-1$.
(B) $1-x$.
(C) $1+x$.
(D) $-x$.
(E) $x$.
(19th American High School Mathematics Examination, 1968)
[Solution] From the given, we have $x-1=\frac{1}{y}$ and $y-1=\frac{1}{x}$.
Or
$$
y(x-1)=x(y-1)=1,
$$

i.e., $\square$ $x y-y=x y-x$, which gives $x=y$.
Therefore, the answer is $(E)$.