Finding inconsistency in a system of equations

Questions
,
1

i am a rookie in Mathematica and apologise in advance. Here is a question - is there any tools , built in the program, of detecting inconsistency in a nonlinear system of equations? Whilst finding an error in {x+y=2, xy=1,x=2} is a simple task, expanding of the size of a system may result in more complex problem

2

Yes, the complexity of the problem can escalate very fast. You may try with

FindInstance[x + y == 2 && x y == 1 && x == 2, {x, y}]

or with

Resolve[Exists[{x, y}, x + y == 2 && x y == 1 && x == 2]]