1968 AHSME Problems/Problem 14

Problem

If $x$ and $y$ are non-zero numbers such that $x=1+\frac{1}{y}$ and $y=1+\frac{1}{x}$ , then $y$ equals

$\text{(A) } x-1\quad \text{(B) } 1-x\quad \text{(C) } 1+x\quad \text{(D) } -x\quad \text{(E) } x$

We see after multiplying the first equation by $y$ , that

$xy=y+1.$

Similarly, we see that after multiplying the second equation by $x$ , we get that

$xy=x+1.$

Thus $x+1=y+1 \implies x=y$ , giving us our final answer of $\fbox{E}.$

~SirAppel

1968 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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