KCL nodal analysis and power dissipation in resistor

[hdp12]

Homework Statement

Here is the homework problem I was given:​

The Attempt at a Solution

Above is the work that I began, however, I have an overwhelming feeling that I am incorrect and also I don't know how to continue to the next part/parts. Would someone please help me?
Thank you
H

 

[axmls]

I haven't checked each part, but I do see an issue: note that in your second equation, you've got a voltage plus a current. Any time you're adding different units, something has gone wrong.

 

[hdp12]

I haven't checked each part, but I do see an issue: note that in your second equation, you' a got a voltage plus a current. Any time you're adding different units, something has gone wrong.

You're right, I can't do that..
Is the Voltage at the second node equal to the Voltage source, since there's nothing in between the Voltage source and the node?

 

[donpacino]

You're right, I can't do that..
Is the Voltage at the second node equal to the Voltage source, since there's nothing in between the Voltage source and the node?

no. there is a resistor AND a voltage source in between the two nodes. If you want to do nodal anlysis you'll need to use a 'supernode'