If no solution for x from some system of equations exists, then does that imply that x (at least within domain of that system) does itself not exist??

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Suppose you're solving an inconsistent system. Since none of the variables can have compatible combination of values, then the answer is No Solution, ⦰. What is the correct translation relating the tuple to this answer? In the common 3- case of $x,y,z$, is it $⟨x,y,z⟩=⦰$ or instead $[x,y,z]∈\{\}$ or are the two expressions equivalent or are neither strictly correct?

Supposing instead that one or more if not all the variables do exist, for simplicity suppo4se that $x,y$ is dependent on $z$; for $z:=f(x,y)$ then would it be apt to think of $z$ as $=0±.. 0±..$, where 0 is analogous to nullset with existence (since addition-subtraction is the lowest order of operations, it should never affect the subsequent expression, unlike as possible with e.g. 1 for multiplicative identity)?