Does the method for finding the intersection of 2 single variable functions work for multivariable functions? I have $2$ multivariable functions $Q(x,y)$ and $P(x,y)$, I was wondering if finding the point of intersection between these 2 functions is as easy as making $Q(x,y) = P(x,y)$ as you would do for most single variable functions.
I know you would have more steps to do after that as there would still be $x$'s and $y$'s, I have everything on one side equal to $0$ but don't really know where to go after that.
Edit: Probably worth mentioning that both the $Q$ and $P$ functions are paraboloids(?) I thought about it and realised that I would have found the parabolic/hyperbolic curve of intersection(?) and I'm asked to find the maximum of the two functions $P$ and $Q$ using the same $x and $y$.
Another edit:
$$P(x,y) = 2x - \frac{2x^2+y^2}{10^6}\quad\text{and}\quad Q(x,y) = 2y - \frac{4y^2+x^2}{2\times 10^6}.$$

Yes, finding the intersection between $P(x,y)$ and $Q(x,y)$ is done by simply setting $P(x,y) = Q(x,y)$. Note that it won't always be just a point (or a finite number of points) though!
