{{Short description|RS Aggarwal}}In [[mathematics]] CONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYCONDITION OF CONSISTENCYandand particularly in [[algebra]], a [[linear equation system|linear]] or [[nonlinear equation system|nonlinear]] [[system of equations]] is called '''consistent''' if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when [[substitution (algebra)|substituted]] into each of the equations, they make each equation hold true as an [[identity (mathematics)|identity]]. In contrast, a linear or non linear equation system is called '''inconsistent''' if there is no set of values for the unknowns that satisfies all of the equations.<ref>{{Cite web|title=Definition of CONSISTENT EQUATIONS|url=https://www.merriam-webster.com/dictionary/consistent+equations|access-date=2021-06-10|website=www.merriam-webster.com|language=en}}</ref><ref>{{Cite web|title=Definition of consistent equations {{!}} Dictionary.com|url=https://www.dictionary.com/browse/consistent-equations|access-date=2021-06-10|website=www.dictionary.com|language=en}}</ref>
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).
