The same circuit is used in the Detailed Nodal Analysis Example.
Step 1: Replace any combination of resistors in series or parallel with their equivalent resistance. Here I simply use the result from the previous example.
Step 2: Choose clockwise mesh currents for each mesh and label accordingly.
Step 3: Write the mesh equation for each mesh. Here I suppress the "k" for each resistor; the final currents will be in milliamps.
|Left mesh:||11 I1 - 6 I2 = 9|
|Right mesh:||- 6 I1 + 18 I2 = 9|
Step 4: Solve the equations to obtain the values of the unknowns. Tackle the solution of the simultaneous equations in your preferred way.
|I1 :||4/3 mA||1.33 mA|
|I2 :||17/18 mA||0.94 mA|