How does one solve the following system of equations in two variables?

Question

I'm trying to solve the following system of equations in $R$ and $m$ for fixed $k>0$ and $l\in\mathbb{R}$: $$ \left\{ \begin{aligned} k&=\frac{R}{m^2+R^2}, \\ l&=\frac{m}{m^2+R^2} \end{aligned} \right.. $$ Is there a method to solve this system of equations? I tried rewriting the first equation to a quadratic one in the variable $R$ in order to use the quadratic formula. But that didn't really get me any closer to the solution, I think.

Answer 1

Note that one has $ml+Rk=1$ and $mk=lR$ from the two given expressions. Now one can solve the system of simultaneous equations.