Next time use Spice
I'm kidding. But Spice can help you check your answers. In fact all that mesh current analysis and stuff like is exactly how computer simulations analyze circuits. They basic create matrices based on the equations such as yatzr posted. Except, you can have a gadzillion unknowns and a gadzillion equations.
I remember doing this stuff back in the day. The dependent current and voltage source stuff was a little weird because they are not really a concrete actual part per say. But later on you'll learn that BJT's are actually current controlled current sources and MOSFET's are voltage controlled current sources.