Two equations with one solution over infinite variables Apparently, my previous question didn't get no satisfactory answer, when I asked for two equations having a fixed value for each, not necessarily linear. As XenoGraff states, WolframAlpha does the task, but counts permutations of values among variables, and is thus impractical to test any two equations.
Actually, I ask, is it possible that there could be a system of X equations that can be solved for more than X variables, all having whole number values, considering that these X equations have an unique solution?
As Gerry Myerson states in the previous thread, there is the unproven conjecture that $x^{5}+y^{5}=N$ will have only one solution for $x,y$ for a given $N$, which can be modified to satisfy $x^{5}+y^{5}=x+y$ for only one set of values for $x,y$.
So... are there any such equations? What about differential equations (I don't understand them, anyway) and multivariates? And Diophantine equations?

You can have $(x-a)^2+(y-b)^2+(z-c)^2=0$, which can be solved for $x,y,z$, viewing $a,b,c$ as parameters.  It works for reals or integers.  Is that what you are looking for?
