Nodal Analysis Problem help (Double Supermesh)

[IonizingJai]

Homework Statement

We are required to find the Node Voltages in the given circuit.

Relevant Equations

Why is the Node current b/w node 1 and 3, I = (V2-V3)/2 , not included in the KCL at Supernode -1,3, which is the equation 1.

That is, for Supernode -1,3 (12V branch) , we do Nodal Analysis and we have (V2-V3)/2 , over the 2 ohm branch.
But this current is not included in the Equation 1 in the solution I have attached(Which is my only source to cross check answers/solution right now.)
Is the solution wrong?

Thanks for help.

 

[The Electrician]

The current I = (V2-V3)/2 doesn't come into play because it's internal to the supernode. It enters node 2 and leaves node 3, so it cancels as far as its effect on the supernode. The given solution is correct.