Consistent and inconsistent equations: Difference between revisions

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In [[mathematics]] and in particularly

in [[algebra]], a [[linear equation system|linear]] or [[nonlinear equation system|nonlinear]] [[system of equations]] is called as '''consistent''' if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, that when substituted into each of the equations, they makesmake each equation hold true as an [[identity (mathematics)|identity]]. In contrast, a linear or non linear equation system is called as '''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).