<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 the 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>

When is a system of linear equation said to be consistent
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