Why is it okay to swap a resistor and source in series?
Each of those two series elements, R1+V1 and R2+V2 are the same if you flip them, right? They still have the same current flowing down the leg, and the voltage drop across the V+R elements is the same in each leg.

The node between R1 and V1 will change depending on which way you flop them, but if you don't care about that node, nothing else in the circuit can even tell, right?







simulate this circuit &ndash; Schematic created using CircuitLab

Another way to look at it:

$$V_a = R\times I + V_b$$

or

$$I = {(V_a-V_b) \over R}$$

Neither of these equation forms change if you change the positions of Vb and R!