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{{Short description|RS Aggarwal}}In [[mathematics]] and particularly minecraft 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).
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