The traditional user of scientific computing prefers to use well proven routines that are recognized by the international scientific community. Among the well-known collections are IMSL, NAG and LINPACK. However, a direct solution method should be used in the case of dense non-structured matrices. If, in addition the co-efficient and the right hand side are integers and an exact solution is desired, the most affordable alternative is to use residual arithmetic on hybrid GPU-accelerated multi-core systems.