Determining Whether a System of Linear Equations Is Inconsistent

Question

I have a question about solving systems of linear equations.

1- Is getting a false equation during the normal process of solving a system of linear equations (e.g. substitution/elimination) is the only way we ensure this system has no solutions?

2- If no, what other ways available?

Thanks in advance!

Answer 1

If we have two equations $A=B$ and $A=C$ where $B\ne C$, then we also know the system is inconsistent, for example.