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{{Short description|Whether or not there exists a set of values to satisfy a given system of equations}}
In [[mathematics]] and particularly in [[algebra]], a [[system of equations]] (either [[linear equation system|linear]] or [[nonlinear equation system|nonlinear]]) 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
If a system of equations is inconsistent, then the equations cannot be true together leading to contradictory information, such as the false statements {{math|1=2 = 1}}, or <math>x^3 + y^3 = 5</math> and <math>x^3 + y^3 = 6</math> (which implies {{math|1=5 = 6}}).
Both types of equation system,
==Simple examples==
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has an infinitude of solutions, all involving <math>z=\pm \sqrt{5}.</math>
Since each of these systems has more than one solution, it is an [[indeterminate system]] .
===Underdetermined and inconsistent===
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\end{align}</math>
has exactly one solution: {{math|1=''x'' = 1, ''y'' = 2}}
The nonlinear system
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