I've spent more than 3 hours with the idea that we should find current across every resistor in terms of i10. This is somehow not working, I mean putting the KCL (Kirchoff's Current Law) equations of different nodes into each other just makes left and right sides equal. It doesn't give any value of i10. The dependent current source only makes it more difficult. Please guide me on the best approach to solve this question or if you're kind enough give the solution. The solution will be highly appreciated!
This easily leads to one more unknown voltage or current than the number of equations, if one tries blindly to apply some systematic method. The missing equation fortunately can be found after a little thinking:
Here we have three node equations and four unknowns. The missing equation here is the fact that V3 = V1-I*R2. By inserting it we have 3 unknowns left and our three node equations are enough.
(stop, I never give full solutions to homeworks)