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This paper is intended to show a general method (inhibition method) that relies on the superposition principle to analyze linear systems and electric circuits, based on hierarchical sequences of more simple topologies with some inhibited elements and on a simple recollecting logic to calculate the final solution from the previous partial and more elementary solutions. The result of the analysis is represented by and stored into a table (called the inhibition sequence table), which thus consists in a kind of database for the system or electric circuit being analyzed. The method follows a hierarchical structuration that is halfway physical (the hierarchical blocks have a nonabstract meaning) and halfway logical (the relationships among the blocks carry out information richer than the hierarchy itself). Once the table is calculated for a particular system, then a little calculation overhead allows some other interesting features, like the possibility to analyze an old circuit with some new branches added by analyzing the new elements only, or like the calculation of exact sensitivities without using derivatives, or like the calculation of the inverse matrix avoiding the usual matrix inversion procedure. A proof of the Inhibition Theorem is given and also some tutorial circuit examples.