The Louvre Tablet from the Babylonian civilization is dated about 1500 B.C. It shows a system equivalent to

\[\left\{\begin{array}{l}x y=1 \\x+y=a\end{array}ight.\]

Solve this system for \(x\) and \(y\) in terms of \(a\). This is not a linear system, and you will need to use the quadratic formula after substituting.