Determine , and using the superposition method.
I. Contribution of the voltage source:
We need to turn off the current source by replacing it with an open circuit. Recall that we do not turn off dependent sources. The resulting circuit is shown below.
In the left hand side loop, we have
and in the right hand loop, it is trivial that
Therefore, . Applying KVL around the inner loop,
Substituting , we have
II. Contribution of the current source:
The independent voltage source must be replaced with a short circuit as shown below.
The resistor is parallel with the dependent voltage source, Therefore, and since , we have . Applying KCL at the right bottom node, . So,
Applying KVL around the inner loop,
III. The final result