Finding currents and voltages in a ladder network with Kirchhoff's laws

[vaio911]

Homework Statement

Find $i_1,i_2,v_A,\text{ and }v_H$ in the ladder network. Calculate the power dissipated in the $2\;\Omega$ resistor.

http://i.snag.gy/PIhxl.jpg

Homework Equations

Kirchhoff's Laws (i.e. current law, voltage law).

The Attempt at a Solution

Ok, I know that I can simplify the circuit down to one loop then use Ohm's law to calculate $i_1$, but then I have to do other things to get the other stuff.

I tried to make a system to solve this problem using the laws.
Can somebody tell me where I'm doing wrong here?

$\begin{align}<br /> i_b&=i_c+i_a\\<br /> i_c&=i_e+i_d\\<br /> i_e&=i_g+i_f\\<br /> 12i_a-28+8i_b&=0\\<br /> 12i_a+6i_c+15i_d&=0\\<br /> 4i_e+10i_f+15i_d&=0\\<br /> 2i_g+13i_h+10i_f&=0\\<br /> 4i_e+2i_g+13i_h+15i_d&=0<br /> \end{align}$

Getting me something like:
$-\frac{7}{39},\frac{49}{13},\frac{154}{39},\dots$

which I know is completely off.

 

[vaio911]

If you can't understand my handwriting,

$V_a$ is the one w/ the 12 ohms.

$V_h$ is the 13 ohms one.

 

[vaio911]

It is because of the direction of the currents?

 

[CWatters]

I'd probably just simplify it. If you keep your working for each step it will help when it comes to working out the voltages using the potential divider rule.