What is the best way of solving the circuit?

The equations for nodal analysis are the easiest to write, and least likely to make mistakes. Using a symbolic algebra program allows for a minimum busy work solution. See attached analysis.

The node equations are written for each of the identified nodes: V1, V2, V3, & V4 with currents I1 & I2. I like the convention that current leaving a node is positive while current entering a node is considered negative. That way the equation for any node always begins (V,node - V,othernode). Note that here V1=100 and I1 is a multiple of (V1-V2)/6 so there are 4 equations and 4 unknowns (V2,V3,V4,I2). Once the initial equations are written, MathCAD makes it easy to solve the system of 4 equations by repeated copying and pasting of substitutions. Algebra manipulations are handled automatically by the 'solve' command. Calculations are done in place and intermediate results are not shown, otherwise the size of the pdf file would exceed the limit for posting here.

 

Possibly. But the OP didn't seem to have sufficient grounding in nodal analysis to be able to know what to do with cryptic hints. The OP seemed to need an example to demonstrate that nodal analysis was possible and even the best way to analyse this circuit. Perhaps I should have constructed the example with slightly different component values in order to demonstrate the method without providing the exact solution. See attached nodal analysis for a modified circuit that illustrates the technique.

 

Or laziness... This isn't just a model he/she whipped up in paint one day for the heck of it, I'll place money on it being a copy out of a homework assignment...

Thus doing the homework and giving the answer does not provide (in your words) the 'sufficient grounding in nodal analysis' that the exercise was supposed to teach or test for...

I agree using different values and even a slightly different model would be a better choice, make the student work the noodle vs cut and paste the answer on his homework... With the advent of the Internet it scares me how many students are getting degrees in stuff that they have little to no understanding of because they cheated there way to answers on the Internet... It's bad enough there are mathematical programs that do all the work for equations and the students likely never learn any advanced math, but giving them the answer flat out only furthers the problem...

 

The OP posted this on at least 2 other forums, and got a solution on one of them right away.

 

And IMO that is sad, a bunch of inept graduates with degrees that they obtained by cheating due to Internet do-gooders that willingly did their homework for them...

 

If by efficient, you mean less work to find a solution, letting a computer do most of the work is about as efficient as it gets.

If you don't care about the current through the 100 volt source, you could use a nodal formulation of 3 equations in 3 unknowns, since the voltage at the node where the 100 volt source is connected is known.

Otherwise, you've got 4 unknowns however you formulate it.

If, on the other hand, you mean compactness of appearance of the solution, the best you can do is to formulate as a matrix solution.

Since Laplace has already done a nodal formulation, go back to the other forum where you were given a mesh solution:

http://forum.allaboutcircuits.com/showthread.php?t=75500

Formulating as a matrix solution, you have what I've shown in the attachment. The only work you, the human, has to do is to set up the problem; the computer does the algebra for you. I don't know how you can get any more efficient that that.

 

You did originally before you edited the post, with some excuse about how you just whipped up this problem for the heck of it... You must have realized how silly that sounded since it's been pointed out you cross posted the thread to multiple forms seeking an answer rather than actually interacting to discover and discuss said answer and how to go about solving it