This paper explores some important characteristics of a system of linear equations containing parameters. Such a system of equations arises in many branches of engineering including electrical circuits, hydraulic networks and truss structures. A parametrized solution of a set of linear equations can be obtained by applying Cramer's rule. In many practically important cases the parameters appear with rank one dependency, resulting in parametrized solutions to be of a rational multilinear form, which will be monotonic in each parameter. This monotonic characteristic has practical importance in the analysis and design of linear systems with parameters having interval uncertainties. In particular, extremal values of system variables occur at the vertices of the parameter boxes.