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If a system of equations is inconsistent, then it is possible to manipulate and combine the equations in such a way as to obtain contradictory information, such as 2 = 1, or ''x''<sup>3</sup> + ''y''<sup>3</sup> = 5 ''and'' ''x''<sup>3</sup> + ''y''<sup>3</sup> = 6 (which implies 5 = 6).
Both types of equation system, consistent and inconsistent, can be any of [[overdetermined system|overdetermined]] (having more equations than unknowns), [[underdetermined system|underdetermined]] (having fewer equations than unknowns), or
==Simple examples==
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