I have an equation in the x-y plane, and another in the z-x plane.
Is it at all possible to combine them into the x-y-z space?
I realize that there might not be enough data to fill the gaps, but I thought of using one of many interpolation methods out there to fill the data (if needed)
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$\begingroup$For this answer, I'll assume that your equations can be put in the form $y = f(x)$ and $z = g(x)$. If not, then the following doesn't apply.
With that assumption, then there is a very natural way to build a curve in 3-d based on your 2-d curves. In three dimensions, the curve $y = f(x)$ actually defines a cylinder, which is just what you get if you 'expand' the curve in the $z$ direction. Similarly, the $z = g(x)$ curve defines a cylinder that expands into the $y$ direction.
The intersection of those two cylinders will be a curve that exists in 3-dimensional space. Its coordinates are quite straightforward too; it will just pass through all the points $(x, f(x), g(x))$.
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