# Simultaneous equation with fractions

Given the system of equations $$\frac{2}{x} + \frac{3}{y} = 6 \quad \text{and}\quad 5x - y = 4$$ solve for $$x$$ and $$y$$.

I have tried rearranging the equation to substitute either $$x$$ or $$y$$, but I wasn't able to solve it. Any help would be appreciated.

Put $$y=5x-4$$ in the first equation and multiply the equation by $$x(5x-4)$$ You will get quadratic equation in $$x$$. Do you know how to solve a quadratic equation?
If you substitute $$y$$ by $$5x-4$$ in the first equation, you get$$\frac2x+\frac3{5x-4}=6.\tag1$$But\begin{align}(1)&\iff\frac2x+\frac3{5x-4}-6=0\\&\iff\frac{-30 x^2+31 x-8}{x (5 x-4)}=0.\end{align}Can you take it from here?