Homework Help: Nodal analysis help

You're right, there's no need for loop equations. In this case just mark out all the nodes, and taking into account the direction of the current in the circuit, calculate the voltage at all the nodes using an arbitrary starting point of 0V in the circuit, remembering to minus potential when you cross over from + to - of a circuit element and add potential when you do the opposite. You should be able to get the potential at the point just above the 2A current source.

From there you can calculate the power absorbed/supplied by the source.

 

I would use KVL and the conservation of energy in a loop for a beginning.Since we know the value of each independent source, followed by convention sign we should be able to figure out how much energy left across the resistor. If the left energy is negative , then it is supplying the power. If it is a positive, then is is observing the power.