In this article, we studied the theoretical investigation of basic enzyme reactions of substrate and product concentrations. The enzyme kinetics helps in drug designing, Drug Metabolism and the determination of disassociation constants for antigen-antibody interactions in solutions. The arising physical governing system we solved by using the general ordinary differential method. The obtained results show the substrate, enzyme, substrate-enzyme, and product concentration profiles are presented with help of graphs and tables. From this study, we found that as increasing substrate value improves the rate of reaction. If the rate constant is greater than substrate concentration, the rate of reaction depends on free enzyme content and substrate amount. In a similar way, the substrate concentration is greater than rate constant the rate of reaction depends only on free enzyme content.