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Age 14 to 16 Challenge Level:
Find the exact values of $x$, $y$ and $a$ satisfying the following system of equations:
\begin{align}
\frac{1}{a+1}&=a-1 \\
x+y&=2a \\
x&=ay
\end{align}
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.