<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>
a system of linear equations is consistent if
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