The Laws of Circuit - you can learn and practice by just reading

copyright. Charles Kim 2006

Test Voltage Method (for Thevenin Resistance Determination)
Test Voltage Method for Thevenin Equivalent Circuit: As the third method of calculating Thevenin resistance of a circuit, the test voltage method is a very powerful tool, since you can minimize the circuit by deactivating any independent sources in the circuit. Therefore, the only independent source is the test source with voltage amount of VT. By the way VT is the voltage of the test source, which means VT is a known value like 2[V] or 10[V] only expressed with letter instead of number. It's like your brother is boasting, "Hey, bro! D'you know how much I made last week? 2K!" And we all know that he means $2000. The letter K is a letter but actually a known number, 1000. In other words, in your equations to solve for VT and IT, treat them as a known number, not as variables. Node voltages in your equations are variables, but not VT and IT. Therefore, solving the problem is, first, to convert all node voltages in terms of VT, and second, express by KCL, IT in terms of VT. Then, your final equation would have only VT and IT. Then get the ratio of VT and IT, and the result is the Thevenin resistance. A piece of cake, isn't it?  A free lunch from your bro would be icing on the cake.