a system of linear equations is consistent if
Consistent and inconsistent equations 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 systemâ€”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.