Understanding Kirchoffs laws [elaborate example]
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I finally found out that I had to use one additional node equation. 

General rule: If there are 'n' nodes, we need n - 1 node equations. If there are 'b' branches, we need b - (n - 1) mesh equations. In the circuit above, n = 4 and b = 6 so this requires 3 node and 3 mesh equations. 

Source: en.wikipedia.org/wiki/Network_analysis_(electrical_circuits). 
Higly recommended article anyway.

Chris