I have two quadratic eqs: \begin{align} \frac1{x} & = 2 + \frac1{1-r} + \frac1{1-x}\\ \frac1{y} & = 2 - \frac1{r} + \frac1{1-y}, \end{align} where $r\in(0,1)$ is a parameter.
I am interested either in a nice relation between $x,y$ that solve each of the equations and satisfy $x,y\in(0,1)$ or any interesting observation on the equations.