I have the following two equations:
\begin{align} 2-3\int_{-\infty}^{y_0} f(x_0,y)\,\mathrm{d}y +\varepsilon x_0=0\\ 2-3\int_{-\infty}^{x_0} f(x,y_0)\,\mathrm{d} x+\varepsilon y_0=0 \end{align} where $x_0$ and $y_0$ are unknowns, $f$ is a pdf.
Is it possible two find $x_0$ and $y_0$ in terms of $\varepsilon$ and $f$? I know this is a very general question, but any help is greatly appreciated. If you think there is a case( for a specific pdf $f$) where it is possible to solve that would also be great.