Today's computing environments are becoming more multifaceted, exploiting the capabilities of a range of multi-core microprocessors, central processing units (CPUs), digital signal processors, and graphic processing units (GPUs). Presented with so much heterogeneity, the process of developing efficient software for such a wide array of architectures poses a number of challenges to the programming community. Linear equations can be used to solve many problems, e.g. solid mechanics, fluid dynamics, structural engineering and so on. Since the size of problems increases to achieve accuracy, number of linear equations to be solved also increases and so is the time. Advancement of new parallel computation technology using inexpensive graphic card processors (multi-core GPUs) makes the dreams coming true to solve large linear equation system of form AX=B. In the present study, a comparison of methods for solving this linear equations system namely Gauss-Jordan Elimination and Cholesky Factorization is presented. Graphics Processing Unit as well as Central Processing Unit is used for parallel computations with help of OpenCL programming language. It is a step in the direction of heterogeneous computing for smarter, faster and better analysis of problem. The main purpose of using this parallel computation is to minimize the time of analysis of problem that involves large number of linear equations. Keywords: Parallel computing, GPU, CPU, OpenCL, Parallel Computing.