An equation with 2 variables (x and y) is observed to be giving a graph of a point or a curve at most, in xy-plane. But since an Equation with 2 variables can give a graph of multiple points (a curve), ain't it make it possible for such an equation to give a graph of a sub-plane (a plane smaller than xy-plane) that lies anywhere in xy-plane ?
I mean we may yet haven't found such a 2 variables-based equation but there is always a possibilty that such entity exists, right?
In case you haven't got me:
If you haven't got me yet here I have something for you that might help. Suppose we have a random equation in 2 variables xy-3x=6, we all know that when we plot these kind of equations in xy-plane, we get a curve. So my question is, can there be a similar equation (equation in 2 variables; x and y) which actually gives us a graph of a plane (surface) when we plot it in xy-plane? I mean, can it (equation in 2 variables) give us the coordinates (x, y) of a rectanglular region or any 2D-region upon solving?