its weird that i got this rite in the exam, but i cant solve it again,
haha heres how i did it.
Ia + Ib = Ic , heres the basic mistake which you did, which caused the whole thing to go rong.
Ia be a, and Ib be b
2-2a-3Ic=0
2-2b-3Ic=0
any 2 above can be used as equation 1
2-2a-3Ic=2-2b-3Ic
3Ic and 2 will get cancelled
you get an equation -2a+2b=0, this will be used as equation 2
now simultaneously solve
i will use loop a, and split Ic current
2-2a-3(a+b)=0
2-2a-3a+3b=0
1)2-5a+3b=0
2)-2a+2b=0
and voila!