We present a case study of parallelizing serial legacy code using Invasive Interactive Parallelization (IIP) - a compositional approach to parallelizing code refactoring rooted in the Invasive Software Composition (ISC) and the Separation of Concerns (SoC). The study focuses on scientific code, in particular, Gaussian elimination where parallelization neither requires nor incurs serious changes in the algorithmic structure. As the major contribution we show how parallelization of Gaussian elimination can be automatized with reusable parallelization recipes implemented as composers in Reuseware. We consider parallelization for both shared-and distributed-memory systems with OpenMP and MPI respectively. We present the speed-ups achieved and discuss gains in code reusability.