An algorithm for analysis of simultaneous multicomponent systems is proposed. This method is suitable for underdetermined systems, where the number of chemical components is larger than the number of measured data points. This method provides a rational solution to such underdetermined cases, with no need of any model assumptions. Such situations are faced, for example, in application of low-cost sensors to environmental analysis, where complex mixtures must be handled. The proposed solution is based on information theory and provides a unique set of concentrations that is the most unbiased one. The algorithm maximizes the entropy of the solution set, which means that the final unjustified information is minimal. Detailed description of the mathematical procedure is provided. The method is exemplified for spectroscopic analysis and evaluated by extensive computer simulations. Several effects, such as the number of components and the number of measured points, the noise level, spectral characteristics, and the sampling design, are studied. The stability of the algorithm and the analytical performance in some cases are evaluated in respect to these factors. Satisfactory results are obtained in systems with realistic noise levels.