Simultaneous equation with fractions

Question

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.

Answer 1

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?

Answer 2

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?