If you use KVL in the other loop (36v i5 and i2) then use that, the other kvl equations and two of the kcl equations it should work.
Adding all the kcl equations should give 0=0. They don't include the voltage so they can't actually solve for anything here.
Can you useUsing star-delta transforms and mesh analysis? That makes can make it a bit easier to solve (transform the delta that doesn't have I1 in it to a star/wye).