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I was wondering about inconsistencies in linear equations.

If I have three equations and four unknowns, and I can make one a linear combination of the other two, then I can identify if there is an inconsistency. If I cannot make one from a linear combination of the other two, how do I identify if there is an inconsistency and therefore no solution, because I may end up with free variables and conclude that there is an infinite number of solutions? Do I have to plug in one of the solutions and see if it solves?

I hope this makes sense.

Any help appreciated.