Linear Algebra - Find current from diagram

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Hey so I tried looking at the example in the book and I understand what to do after I find the linear equations, in order to find the currents in the diagram, but I cannot for the life of me figure out what the equations are..

Any help would be greatly appreciated..

 

[Deleted member 4993]

Hey so I tried looking at the example in the book and I understand what to do after I find the linear equations, in order to find the currents in the diagram, but I cannot for the life of me figure out what the equations are..

Any help would be greatly appreciated..

Apply Kirchoff's Laws