Having trouble with some review circuits using nodal analysis

[mitchapalooza]

Having trouble with some review circuits using nodal analysis :(

Homework Statement

I'm trying to find node voltages for v1, v2, and v3.
I = 3.1A

Homework Equations

V=IR

The Attempt at a Solution

My method of going about and solving this was fairly straight forward I thought. The way the question is set up, I believe nodal analysis is already ready to go. So I started with
KCL(v1): 2 + 3.1 + (v1-v2)/3Ω = 0
KCL(v2): (v2-v1)/3 + v2/2 + (v2-v3)/4 = 0
KCL(v3): (v3-v2)/4 + v3/3 - 3.1 = 0

Now it's been a while since I've done this (nodal analysis), but I now have 3 eqns and 3 unknown variables. The answer I have is -21.2V -5.87V and 2.8V respectively.

It's one of those, "I've tried all my guesses, need some reassurance before I commit to my last chance" scenarios.

Any helpful on this would be great! Thanks :D

Note that I haven't tried the brute force method of just solving for everything, or the mesh current method.

 

[NascentOxygen]

Hi mitchapalooza, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

The answer I have is -21.2V -5.87V and 2.8V respectively.

Have you substituted those back into the equations to verify they are the solution? The equations look right.

 

[rude man]

Have they taught you the superposition theorem? That way you could handle the problem one current source at a time ...

 

[alod]

I solved the system and found v1 = -20.78V, v2 = -5.78V and v3 = 2.67V

 

[rude man]

I got
V1 = - 21.17
V2 = -5.87
V3= +2.80
so we're close.

 

[The Electrician]

Well, I got:
V1 = -127/6
V2 = -88/15
V3 = 14/5

which is the exact solution.

The 12 digit floating point approximation would be:

V1 = -21.1666666667
V2 = -5.86666666667
V3 = 2.80000000000