Node voltage Analysis with voltage controlled voltage source

[forsaken231]

Homework Statement

Here is the circuit
http://i.imgur.com/Xn2mc.jpg

The Attempt at a Solution

I've tried it a few ways, but the one I'm going for at the moment is this

Node 1: (v1-v2)/10 + (v1-v3)/15 + v1 /5 = 1
Node 2: (v2-v1)/10 + (v2-v3)/10 + v2 / 5 = 2
Node 3: 2Vx where Vx = (v2 - v1)/10

When I solve I don't get the correct answers:
Node 1: 5.405V and Node 2: 7.297V

I tried doing equations without a 'node 3' involved but they just didnt work out either. If i DO only need to use 2, please explain to me how to do so, I'm really stuck :(

 

[lewando]

Don't have time to dive into this thing yet, but this is not helping:

Node 3: 2Vx where Vx = (v2 - v1)/10

should be v_x = v₂ - v₁

 

[forsaken231]

You're a lifesaver, figured it out.
It's always the small things that get me, stupid dependency equations.

Thank you :)

 

[rude man]

I assume you dug up the 4th equation? 4 unknowns need 4 equations: v1, v2, v3, vx.
Of course, the 4th is obvious ...

 

[forsaken231]

haha i had the 4th equation i just wrote it wrong >.<