Q:  Determine the value of I₁ from the circuit.

Solution:          We can redraw this circuit like this

By applying Constraint equation for the super node

                                                V₂ - V₁ = 6Volts

By applying KCL equation for the super node

    ((V₁ - 3)/6k) + (V₁/12k) + (V₂/12k)+ ((V₂ +3)/12k) = 0

                  2V₁ -6 + V₂ + V₁ + 3 + 2V₂ = 0

                              3V₂ + 3V₁ = 3

                                  V₂ + V₁   =1

By adding constraint equation and KCL equation

                                V₂ - V₁=6

                               V₂ + V₁=1

                                        2V₂ = 7 

 Or

                 V₂ = 3.5volts

                    I₁ = 3.5/6k

                    =35/60k    =7/12 mA                   Ans.