<Table> <Tr> <Td> </Td> <Td> This article does not cite any sources . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (April 2018) (Learn how and when to remove this template message) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This article does not cite any sources . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (April 2018) (Learn how and when to remove this template message) </Td> </Tr> <P> In mathematics and in particular in algebra, a linear or 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 . In contrast, an equation system is inconsistent if there is no set of values for the unknowns that satisfies all of the equations . </P> <P> 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 + y = 5 and x + y = 6 (which implies 5 = 6). </P>

A system of linear equations is consistent if