Q:      Calculate the currents I₁,I₂ & I₃.

Solution:    We have to determine the currents I₁,I₂ and I₃.. The circuit may be redrawn like

                        For mesh 1

                                    4I₁ -4I₂ +1 = 0 ............A

            For Super mesh (mesh 2 & mesh 3)

                                    2I₃ + 3I₂₊ 4I₂ - 4I₁ =  0 .........B

            Now Coupling Equation is

                                                             I₃ - I₂ = 2 V_X

            In this circuit

                                                                 V_X =  3I₂

            By solving out equation 1

                                                            4I₁ - 4I₂ = -1

            By solving out equation 2

                                                              - 4I₁ + 7I₂ + 2I₃ = -1

            In the circuit for Mesh 3      

                                                              -7I2 + I₃ = 0 ..............C

            Solving equation A,B and C

                                                            I₁ = - 308.8 mA

                                                             I₂ = - 58.82 mA

                                                            I₃= - 411.8 mA