What are the equations for calculating loop currents in a circuit?

[theuniverse]

Homework Statement

Find the Loop currents that are shown in the network of the figure below.

Homework Equations

V=IR

The Attempt at a Solution

I know that I need to create 3 equations since there are three unknown currents and then solve for them so here is what I got.
1) $$10V-5I_1-2I_1=0$$
2) $$10V-5I_3-3I_3-20V-4I_3+4I_2=0$$
3) $$4I_2-4I_3+2I_2=0$$

When I solve for the currents I get
$$I_1=1.43A$$
$$I_2=-0.71A$$
$$I_3=-1.07A$$

While the correct answers should be 3.55A, -1.98A, -2.98A. I suspect that my equations are incorrect but I can't come up with any equations that give me the right answer or make any sense.

Thanks,

 

[gneill]

As you 'traverse' each resistive component in a given loop, you need to take into account all the currents flowing through that component. So, for example, the voltage drop across your 5Ω resistor is (I1 + I3)*5Ω.

 

[theuniverse]

Yea that was the concept I couldn't fully understand... I get it now.
In case anyone else is interested here are the equations that actually work:
1) $$10V-5I_1-2I_1-5I_3=0$$
2) $$10V -5I_1-5I_3-3I_3-20V-4I_3+4I_2=0$$
3) $$4I_2-4I_3+2I_2=0$$

gneill You've been a great help as usual! Thanks!