Solutions for the given system with fractions I have to solve in $\Bbb{R}$ the following system :
$$
\ \left\{
    \begin{array}{ll}
        \frac{y}{x}+\frac{x}{y}=\frac{17}{4}  \\
        x^2-y^2=25
    \end{array}
\right.$$
For this one I am stuck, I tried to use the fact that $x^2-y^2=(x-y)(x+y)$ and multiply by $x$ (or $y$) in line $1$ but fractions 'bother' me. Any hint are welcome.

Multiplying by $4xy$ gives $4x^2+4y^2=17xy$ or $4x^2-17xy+4y^2=0$, so
$(4x-y)(x-4y)=0.$
Now substitute $y=4x$ and $x=4y$ into the second equation to find the possible solutions.
