superposition
Superposition is a divide-and-conquer trick for circuits that have more than one source. It says that in a linear circuit, the total voltage or current anywhere is just the sum of the contributions each source would produce on its own, with all the other sources switched off. Rather than wrestle with every source pushing at once, you let them take turns, work out each one's effect separately, then add the results.
The procedure is to consider one source at a time. Turn off every other source, which means replacing other voltage sources with shorts and other current sources with opens, exactly as in finding a Thevenin resistance. Solve the simpler one-source circuit for the quantity you care about. Repeat for each source in turn, then add all the partial answers together. For example, if one source alone would put 4 V at a node and a second source alone would put 1.5 V there, with both active the node sits at 4 + 1.5 = 5.5 V.
Superposition is a cornerstone of linear circuit theory and underlies why Thevenin and Norton equivalents work at all. But there is a sharp and important honesty here: it works only for linear circuits, and you may only superpose voltages and currents, never power. Power depends on voltage or current squared, and squaring is not linear, so you cannot find each source's power separately and add them. To get power, first superpose to find the total voltage or current, and only then square.
A node is driven by a 9 V source through one resistor and by a 6 V source through another. Solve with only the 9 V active (the 6 V shorted), then only the 6 V active, and add the two node voltages to get the real one.
Let sources act one at a time, then add their effects, but only for voltage and current.
You may superpose voltages and currents, never power. Power goes as the square, so add the contributions first and square afterwards. And it only works for linear circuits.