<p>If <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" /> and <img alt="$y$" height="13" src="https://latex.artofproblemsolving.com/0/9/2/092e364e1d9d19ad5fffb0b46ef4cc7f2da02c1c.png" width="11" /> are non-zero numbers such that <img alt="$x=1+\frac{1}{y}$" height="40" src="https://latex.artofproblemsolving.com/4/0/0/4005f84d470c2e41bf6b7fb26f222c8b2a145469.png" width="78" /> and <img alt="$y=1+\frac{1}{x}$" height="37" src="https://latex.artofproblemsolving.com/d/9/5/d959883afa360e3e83c4a75bccbf66beb618707c.png" width="77" />, then <img alt="$y$" height="13" src="https://latex.artofproblemsolving.com/0/9/2/092e364e1d9d19ad5fffb0b46ef4cc7f2da02c1c.png" width="11" /> equals ?</p>

Question No: 225

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

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Tags: Algebra Probability

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