And everything else is given to us so we can solve for each one of those voltages.

[COUGH] We also need to find an equation

that relates V sub x to the unknown voltages V1, and V2, and V3.

because in fact, the independent current source adds yet

another a invariable V sub x.

So we need to find the relationship between V sub x,

our controlling parameter and our nodal voltages.

And if we look at the circuit, it's quite easy to find that constraint equation.

And we know that V1 = V sub x.

So now we have our four equations and

our four unknowns if we include our unknown from the dependent current source.

So we can solve these simultaneously.

Openly, we see the V sub 0 = V sub 3.

It's the same voltage.