Consistent and inconsistent equations: Difference between revisions

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In [[mathematics]] and in particular in [[algebra]], a [[linear equation system|linear]] or [[nonlinear equation system|nonlinear]] [[system of equations]] is '''consistent''' if there is at least one set of values for the unknowns that satisfies every equation in the system—that is, that when substituted into each of the equations makes each equation hold true as an [[identity (mathematics)|identity]]. In contrast, an equation system is '''inconsistent''' if there is no set of values for the unknowns that satisfies all of the equations.

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''³ + ''y''³ = 5 ''and'' ''x''³ + ''y''³ = 6 (which implies 5 = 6).