The third system has no solutions, since the three lines share no common point. The second system has a single unique solution, namely the intersection of the two lines. The first system has infinitely many solutions, namely all of the points on the blue line. The following pictures illustrate this trichotomy in the case of two variables: In the first case, the dimension of the solution set is, in general, equal to n − m, where n is the number of variables and m is the number of equations. Such a system is also known as an overdetermined system.
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