Unique solution of an overdetermined system

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If I want to know how many solutions a consistent linear system with more equations than unknowns has, how do I tell? Obviously there is either 1 solution of infinite solutions. Can you have a free variable in this case? I'm confused how to find out whether a system will give a unique solution.
 

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HallsofIvy
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You need to determine how many independent equations there are. If the system really is consistent, then there must be no more independent equations than unknown variables. That is, if n is the number of variables and m is the number of independent equations, then [itex]n\ge m[/itex]. The number of free variables is n- m.

If you write the coefficient matrix for the system and row-reduce, the number of independent equations is the number of non-zero rows.
 

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