Is it possible to create a system of two equations with 3 variables and only one solution? I know that a system of equations with 3 variables usually has to contain at least 3 equations, but are there any special cases where 2 equations with 3 variables have just one solution? I've researched a bit, and found 2 equations with 3 variables with finite solution sets, but are there any that have exactly one solution? The equations could be linear or quadratic or cubic or sinusoidal or anything... but does such a case exist?
Also, is it possible to find such a case if we know any 2 variables? Like, for example, $a + b + c = w$ and $b + c = d$, given b and d. (of course, this example has more than 1 solution, but are there any like this that have just 1 solution)
Thanks for any help!
Edit:
To clarify, I'm looking for the general form of such an equation. To be more specific, are there any systems of 2 equations, with 3 variables, that only have 1 solution, but which can be modified to have any 1 solution I desire.

Yes there is.
$x^2+y^2=0$ and $z=0$.
Edit:
$(x-a)^2+(y-b)^2=0$ and $z-c=0$
