Parallel resistor not affecting rest of the circuit
I'm not going to just give you the answer to your homework problem.

However, consider what it really means to be a voltage source.  Let's say I have a 6V source that is good to 1 A.  What voltage is it when nothing is connected?  When I put a 60 &Omega; resistor accross it?  A 30 &Omega; resistor accross it?

If I put the 6 V source and resistor inside a black box and brought out only the two leads, what difference could someone observe on the outside to distinguish the no load, 60 &Omega; and 30 &Omega; cases?  Now consider this is the case you have.  Your +6V and R are inside the box and the rest of the circuit on the outside.