A line loss approximation via parametrization is developed to improve performance of the simplified Baran and Wu DistFlow method, while maintaining a linear set of equations. The approach is evaluated on thousands of training feeders that are created to determine a numerically optimal setting for the parameterization. Feeders are generated using recent advances in synthetic network test case generation. The problem is formulated with the same structure as the simplified DistFlow, yet is more accurate given that line losses are explicitly expressed and quantified. The single-phase methodology is extended to multiphase systems by formulating matrix-vector equations that maintain an analogy to their single-phase counterpart. Results with approximated line losses are shown to also improve the accuracy of multiphase distribution system calculations.