This procedure is tedious, but it requires very little fancy math and it's conceptually beautiful. You ought to be able to look at the finished product and explain WHY the values of voltage drops and currents for each resistor and combination of resistors have the relationships they do. Yay! You can now simplify any circuit with just one battery and a bunch of resistors...or can you? Those in the know call this finding the Thevenin Equivalent circuit, 'cause the method was proven by Thevenin long ago.