I am a bit confused about problem 5P in chapter 3 in the book basic engineering

Question

I am a bit confused about problem 5P in chapter 3 in the book basic engineering circuit analysis ninth edition (J.David Irwin and R. Mark Nelms)...As I am working through the solution provided by cramster, I am confused about STEP 2 (doing a nodal analysis through node V_2). Why is it that in step one, the current is going OUT of V1 and yet in step two, the current is going OUT of V2...I thought you had to remain constant with your current convention. Am i mistaken? Any help would be greatly appreciated.

Explanation / Answer

infact in both cases . you have to assume the direction ofcurrent. either you take the current flowing out of the node orflowing into the node. but you have to remain constraintthroughtout the question. the kcl equatiuons you write by assuming the direction ofcurrent will be remain same either you take current inside the nodeor outside the node but only the difference of minus sign. you can take both either current flowing into the node oroutside the node but this direction must be remain constantthourghout the question. arbitrary but consistant method.

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