According to the conventional perception among engineers, once a circuit is reduced to its Thevenin or Norton equivalent, the voltage and current may be determined only at the load, but not in the remaining parts. The other voltages and currents that exist in the remaining parts of circuit should be determined by returning to the original circuit; substituting the solutions obtained at the load location; and then employing the rules of circuit theory. In this paper, we presented a source equivalence theorem wherein such a back-substitution is never need. It splits an original circuit into two sub-circuits that can be solved separately by using different techniques. Then the voltages and currents everywhere in the circuit can be obtained as a sum of the solutions those two sub-circuits without making any back-substitution.