So looking at node two.

Summing the currents into node two,

we see we have six milliamps falling into node two from the bottom up to node two.

We have the current flowing through the four

kilohm from node one to node two through the four

kilohm that's V1- V2 over 4 kilohms.

And we have the current flowing from right

to left through the 3 kilohm resistor so

that's V3- V2 over 3 kilohms.

That's all of our currents, so the sum is equal to 0.

So when we look at our equations now,

we have two equations and three unknowns, V1, V2, and V3.

So we need our third known equation so

that we have a set of equations which equals our sort of unknowns.

We have three independent equations and three unknowns, V1, V2, and V3.