Trouble finding R in a super mesh
Lots of bad advice on this page, so I'm going to answer this even after all this time.

First, you don't have any supermeshes. By definition a supermesh is closed path that does not include a current source on its edges. There are no such paths here.

Furthermore, by inspection I2 = -2A and I3 = -1A. So the current through R5 (going up) is 1A. Also, by KCL, I1 + 2A = 6A. So I1 = 4A.

To find the voltage drop across R5 you need to find two paths form a ref node to both ends of R5 such that these paths pass only through resistors other than R5 (i.e. these paths cannot pass through R5 or any current sources). No two such paths exist. Which means the value of R in this circuit is not fixed/determined by rest of the components (including the current sources).

To convince yourself, assign some arbitrary value to R5 and solve the circuit, say in a simulator to save time. And then try to assign some other value to R5. The circuit is still solvable, you'll just get another voltage drop across R5.




You can even try it yourself here.