Find I_x, I_y, and I_z in the network.
Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010.
We will write Kirchhoff’s current law for each of the nodes that we picked (picked arbitrarily, pick ones that are the easiest to write equations for). (Forgot Kirchhoff’s current law?)
The negative values tells us that the way we represented current leaving or entering a node is the opposite of what we chose.
This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.18.