Is this supernode equation setup right or wrong ?? Plus most of the eqns used

[MathWizard]

I'm just reviewing superpostion of nodes and meshes, before trying some Modified Nodal Analysis, and Newtons method on systems of non-linear equations. But a few of them I'm getting wrong and I can't find the mistake on paper or in the spreadsheet where I'm doing the calculations.

So here's an example, that was even more right a moment ago, but V2 was wrong, but then I found a silly mistake, and now all node voltages are more wrong.

And it's SUPERNODE(1+3)

The other morning I put the instant coffe in the kettle, instead of the water, but that was due to thinking about ladies...

[MathWizard]

Ok why do I have the 2* in i5=2*G5*V3, thats wrong, probably because the last time I tried the problem, I called Vb=2*Vx, V3

I'm glad this isn't some mid-term

[ledtester]

SUPERNODE (1+2)
ENTERING = LEAVING

(i2 + ia) + (i4 +iv) = (i1 + iu) + (i5 + ia)
...

w.r.t. supernode 1+2, i2 is an internal current and so it shouldn't appear in the entering = leaving equation.
(Or, it both enters and leaves the supernode.)

[MathWizard]

Yeah I saw that right away, thats just a typo it's node1+3

Now after fixing the big mistake, which was just G9 should equal = G4+G5, now it works. So without my extra composite G's which aren't labelled the best, since I was just trying to save myself page space as I went

for node 2, eqn 1 would be
-(2*G3 + G4)*Va = -(G2 + 2*G3 + G4)*V1 + (G2 + 3*G3 + G4)*V2

and the supernode (1+3) would give eqn 2
iv - iu + (G4 + G5)*Va = (G1 + G2 + G4 + G5)*V1 - (G2 + G4)*V2

now finally it works, but I tried it 2-3 times and probably just had a silly mistake each time.

I need to be more careful, I was worried the method was wrong, and just working by fluke sometimes, so I thought maybe my assigned currents had to match the way I used them at node 2 or IDK...and in this case I did make them match