What are the conditions for the existence of real solutions for the following equations:
$$\begin{align} x^2&=a\cdot y+b\\ y^2&=c\cdot x+d\end{align}$$
where $a,b,c,d $ are real numbers.
These represent two parabolas; how might we find out the conditions for the existence of $0,2,4$ real solutions of the equations?