# How to solve the following system

$$\begin{cases}xy + \frac{4}{xy} = 4 \\ 2x-y \; \;= 4 \end{cases}$$

Rearrange the first equation to find $$(xy-2)^2=0\iff xy=2$$
$$4=2x-y=2x-\dfrac2x$$
Rearrange to form a Quadratic equation in $$x$$