The current multi-core architectures have become popular due to performance, and efficient processing of multiple tasks simultaneously. Today’s the parallel algorithms are focusing on multi-core systems. The design of parallel algorithm and performance measurement is the major issue on multi-core environment. If one wishes to execute a single application faster, then the application must be divided into subtask or threads to deliver desired result. Numerical problems, especially the solution of linear system of equation have many applications in science and engineering. This paper describes and analyzes the parallel algorithms for computing the solution of dense system of linear equations, and to approximately compute the value of using OpenMP interface. The performances (speedup) of parallel algorithms on multi-core system have been presented. The experimental results on a multi-core processor show that the proposed parallel algorithms achieves good performance (speedup) compared to the sequential.