Chapter 8.1, Problem 86PE

For Exercises 85-86, use the substitution $u=\frac{1}{x}$ and $v=\frac{1}{y}$ to rewrite the equations in the system in terms of the variables $u$ and $v$ . Solve the system in terms of $u\text{and}v\text{.}$ Then back substitute to determine the solution set to the original system in terms of $x\text{and}\text{y}\text{.}$

$\begin{array}{l}-\frac{3}{x}+\frac{4}{y}=11\\ \frac{1}{x}-\frac{2}{y}=-5\end{array}$