Systems of linear equations, characterized by uncertainty in their parameters, play a crucial role in various problems in economics and finance. In this paper, we explore fuzzy systems of linear equations, where the coefficients are represented as fuzzy numbers. We utilize a Sparse Matrix Techniques to address the uncertainties inherent in these systems. Additionally, we apply LU Decomposition techniques to transform the fuzzy matrix A in the equation Ax = b into two triangular fuzzy matrices, L and U, such that A = LU. This dual approach allows us to effectively solve the fuzzy system of linear equations, combining the strengths of Sparse Matrix Techniques for handling non-linearities and the structured method of LU decomposition for linear transformations.