In [63] the standard form of a system of linear PDEs is used as the basis of an algorithm to recursively solve systems of linear PDEs in their coefficient field by decoupling and solving ``ODEs''. As an application of this algorithm we show that: If the solution space of a system of linear PDEs is finite-dimensional and the coefficients of the system are all rational functions of the system's independent variables, then all rational function solutions of the system can be determined.