# SuperNode Problem

I'm still having problems with supernodes. Correct me if my logic is wrong.

I took the KVL of the circuit which was $-v_1 +2V_o + V_2 = 0$;

Afterwards, I did the nodal analysis of both the incoming and outgoing currents from both sides, which I wrote out as

$$2 + \dfrac{v_2 - v_3}{8s} = \dfrac{v_1 -v_3}{2s} + \dfrac{v_1}{s} + \dfrac{v_2}{4s}; v_{13} = 13$$

next I made $\dfrac{vs}{4s} = V_o$. Is this the proper way to go about the problem?

I get $16s - 39 = 12v_1 -v_2 +8sV_o$ as the second equation.

The first issue you have is that the values of your resistors are given in Siemens rather than Ohms, as shown by the units "S" instead of "$\Omega$". Siemens are the unit of conductance, the inverse of resistance.
$I = GV$
$I = V/R$.
For example, the current through the 1 S resistor is $(1\space\mathrm{S})\times{}v_1$, not $\frac{v_1}{1\space{}\Omega}$. This will dramatically change your results.