Is it possible that the system of equations corresponding to a linear electric circuit has infinite or no solutions?

When using Kirchhoff’s circuit laws and Ohmn’s law to model the system of linear equations corresponding to an electric circuit (so far, circuits involving resistors and sources only), I haven’t been able to find any circuit that yields an inconsistent system nor a system with infinite solutions, thus I was wondering if it were possible that the resulting system of equations didn’t have an unique solution, and if so, what would be the physical interpretation for such result. Also, in case it is not possible, what would be the scientific result that supports that fact. For the sake of clarity, I attatch an example of the kind of circuits I have been working with and its corresponding system of equations.