# Determining Whether a System of Linear Equations Is Inconsistent 1- Is

Determining Whether a System of Linear Equations Is Inconsistent
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?
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Tatiana Gentry
If we have two equations $A=B$ and $A=C$ where $B\ne C$, then we also know the system is inconsistent, for example.
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nidantasnu
Would you count gaussian (aka row) elimination as a possibility? Then there's no solution iff you get a row of zeros except a nonzero at the far right in the augmented matrix that you're doing row elimination on.