120v vs 240v neutral
In a 120/240V system, the neutral is a center tap on a 240 volt transformer secondary coil. So your home is not fed by two 120 volt wires, it's fed by a 3-wire 120/240V single split-phase system.



If it helps, you can think of it as three separate circuits.  There's the 240 volt circuit, which flows through the whole secondary coil (L1 to L2).  Then there's the first 120 volt circuit, which flows through half of the secondary coil (L1 to neutral). Finally  there's the second 120 volt circuit, which flows through the other half of the secondary coil (L2 to neutral).  

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