I've been trying to solve this problem for like 3 hours.
i can't see what i am doing wrong.

here is my result:
http://i69.photobucket.com/albums/i49/yamakasi_i/Untitled-1-3.jpg


could it be the current directions ?
help?

 

could it be the current directions ?
help?

Yes, exactly!

In the second equation at node 2, the current in R3 is written with the wrong sign. The voltage across R3 is (0-V2)/R3, or -V2/R3. This is because you have defined the arrow to be from ground into the node V2.

You are free to define the current direction arrows anyway you like, and you are free to choose your current direction convention, but you must be consistent, as you know. In this case you are using a positive current convention, hence you must define all current directions as going from positive voltage to negative voltage. Your placement of the arrow on R3 forces you to consider ground as the positive terminal on R3 and V2 as the negative terminal.

 

Oops, this got answered while I was doing the math!

 

Thanks!
now it makes sense, i was ignoring the fact that the current will flow for higher potential to lower potential, that's why the current flowing through R3 should have minus sign according to my current direction conventions.