This paper notes the rapid advances that have been made in the modeling estimation and applications of systems of demand equations in the literature. It attempts to empirically estimate for Ethiopians data sets using a two period price information following Pollack and Wales (57) Dybrig (31) ,and a saving information as in Liuch (46) and Howe (41) to identify all parameters of the Liner Expenditure System (LES) and The Extended Liner Expenditure system( ELES) respectively. In spite of the theoretical and empirical limitations of the LES Parameter estimate were found to accord with the right sign and magnitude required by the choice theory Of particular interest is the process of estimating directly the Frisch parameter and its welfare implications The paper also discusses the estimation of compensated and uncompensated own-and - cross price elasticity's in the context of Slutsky decomposition some areas of future research are pointed out in exploiting fully budget studies so far generated in Ethiopia Notably, the possibility of estimating some generalized expenditure systems may stimulate interest for applications to some police issues.