Use the second Kirchhoff's rule (the loop rule) to write two more equations for the circuit. Any two loops in this circuit will give you two independent equations. For example, you can use a-b-c-f-g-a loop and b-d-e-c-b loop. The equation for a-d-e-f-g-a loop, should you decide to write it down as well, will not be independent of the two other loop equations. Now you have three independent algebraic equations (one from application of the junction rule and two from the loop rule). They contain three independent unknown variables (the three currents: I1, I2, and I3)