Hello everyone, having troulbes applying Kirchoff's Rule~DC circuits

[mr_coffee]

Hello everyone, this is my first problem dealing with Kirchoffs Rule and I thought I did it right...here is the circuit...
http://www.webassign.net/hrw/hrw7_27-40.gif
the info is the following:
In Figure 27-40, the resistances are R1 = 1 , R2 = 2.2 , and the ideal batteries have emfs E1 = 2.0 V, and E2 = 3 = 3 V.


Fig. 27-40

(a) What is the current through each battery? (Take upward to be positive.)
battery 1 A
battery 2 A
battery 3 A

(b) What is the potential difference Va - Vb?
V

I came out with the following 3 equations:
E1 + (-R1)(I_1) + R2*I_2 - E2 -R1*I_1;
-R2*I_2 + R1*I_3 - E3 + R1*I_3 + E2;
I_1 + I_2 + I_3 = 0;

When i solve for I_1 = -I_2 -I_3
Where do I plug I_1 into? i tried the first equation and i couldn't solve for any I, and i can't for the 2nd, because there is no I_1, did i do this right? thanks!

 

[Fermat]

Substitute for I_2 = -I_1 - I_3 into both the first two eqns, since it is common to both.
Then you will have two eqns in two unknowns.

 

[mr_coffee]

Thanks! that worked out great, but I messed somewhere writing out the 2nd circuit on the right...This is the equation i got and the work:
http://img477.imageshack.us/img477/956/lastscan6lq.jpg
its wrong...
The first one, i did, on the left, was right though. Any help would be great.

 

[Fermat]

On your last line - in the attachment - the -R₁.I₂ should be +R₁.I₃.

It looks like this mistake was copied through from the line before it.