Reciprocal substitution I

Optional extension

Given that \(m=\frac{1}{x}\) and \(n=\frac{1}{y}\), the variables \(m\) and \(n\) satisfy the following pair of simultaneous equations.

\(m+2n=4\)

\(3m-n=5\)

1. Solve the simultaneous equations to find \(m\) and \(n\).[3]
2. Hence, find \(x\) and \(y\).[2]