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If you look at the node-voltage equations, you see that current of 2ohm-resistor is towards v2 node. How is that determined? If I change the direction the ends of the voltage on that resistor and make the current go the other way, only the third components of two equations change sign and that makes another value arise for i1. So I think it does not depend on my choice and has a special way to determine.

Thanks in advance.

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    You just make a choice and then solve the equations. If you got it wrong you'll get a negative value for the current but that doesn't matter - it's a positive current in the opposite direction. – Finbarr Nov 07 '17 at 10:57
  • Thanks for your comment. I just realized that if you sum two equations from top to bottom, third components(which are related to current of the 2ohm-resistor) will destroy each other on the way. If you change the direction of the current, these two components will have their signs reversed and will still destroy each other on the way they are summed.

    So it doesn't really matter. But I admit that I screwed up on solving equations both ways according to my first post.

     –  Nov 07 '17 at 11:05
  • "Destroy each other" is a bit dramatic! We'd normally say they cancel each other out. – Finbarr Nov 07 '17 at 11:06

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The directions you pick when defining the current direction for the purpose of the equations are arbitrary. If after analysis the current is found to go the other way, the value will simply be negative.

There is no problem with that. Pick a direction to start with, and let the math work out how it works out.

Put another way, -2 A right to left is the same as +2 A left to right.

Olin Lathrop
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