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Step 1: Label currents using point rule I2 = 3I1 - 5 -> I2 = -2A
Step 2: Write loop rule equations 0 = -12 + I1 - 5.5(3I1-5)
0 = - 1V - (I1-I2)1 + 6V - I12 0 = -12 + 27.5 + I1 - 16.5I1
0 = - I23 - 12V - I21.5 + (I1-I2)1 0 = 15.5 - 15.5I1 -> I1 = 1A
Step 3: Solve Step 4: Check point and loop rules
0 = 5 - 3 I1 + I2 0 = -1 -3 +6 -2 (left loop)
0 = -12 + I1 - 5.5I2