Equations 5.31 can be solved using the approach of equations 5.27 and 5.18, by
changing W to U and Z to S and using the definitions of the constants given in equation
5.30 in equation 5.27.
It should be apparent that there are infinities of solutions to this three-position synthesis
problem as well. An inappropriate selection of the two free choices could lead to
a solution which has circuit, branch, or order problems in moving among all specified
positions. Thus we must check the function of the solution synthesized by this or any
other method. A simple model is the quickest check.