We can only come up with four equations for this circuit,

the four nodal equations associated with the nodes.

So, we would end up with five unknowns, and four equations, and

would not be able to solve the problem, because we have too many unknowns for

the number of equations that we have.

So, in order to this problem,

we have to utilize the concept of a supernode to solve it.

And we use this supernode concept when we're doing nodal analysis and

we have circuits where voltage sources are floating between

two nodal points, where 1 ohm is not a reference node.

So, in this case, the 12 volt source is between V1, or between node one and

node two, and neither one of those nodal voltages are known.

They're unknowns at this point.

They're variables at this point.

So, we're going to identify our supernode first.

And our supernode is the node that encompasses our node 1,

it encompasses node 2, and the 12 volt source as shown in the dash line.

So that is our supernode.