Intro to circuit analysis, Solve all the loops in this current? help

[nchin]

I was able to solve this pretty easily using mesh analysis, but what other ways can you use to solve this circuit?

http://imageshack.us/photo/my-images/259/circuita.png/

 

[NascentOxygen]

Instead of those mesh currents, you could mark the current through the 1 Ohm resistor (call it I₁) and using Kirchoff's Laws determine equations around the circuit all in terms of I₁. Once you have an equation with only that single unknown, solve for I₁. You can then find all circuit parameters.