A polynomial equation in two variables typically has infinitely many solutions, in the form of pairs (x, y). That's what we call the graph of a curve. But maybe that's not what you have in mind.
If the multi-variable equation is y=x2 or y/x2=1, there are infinitely many solutions. In fact all the points on the curve of y=x2 are solutions.
This will generally be the case but not always as x2+y2= 0 has only one point and x2+y2= -4 has no points (solutions)
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