And so if we look at the supernode, we can easily see that for

the supernode are constrained equation for our supernode.

Is going to be V1- V3

= 12 volts.

So now we have four equations and we have four unknowns V1, V2, V3, and V4.

Ultimately what we're looking for

in this problem is we're looking for

I sub 0, I sub 0 is related V sub 3.

If we were to write the equation for I sub 0, we see that I sub 0

= V3 minus the ground voltage, so that's coming down through,

from V3 down to ground through the 2 kilohm resistor that's our I sub 0.

So if we're looking for I sub 0, really what we're after is V sub 3.

Because once we find V sub 3, we can solve for I sub 0.

Right now we know of V2 is is minus 6 volts and we know of V4 is it's 12v but

we don't know what V1 is and we don't know what V3 is.

So we're going to solve our set of equations for V3.

And if we do that, we end up with a V3

which is equal to minus six-sevenths of a volt.