1. The problem statement, all variables and given/known data Look at the circuit given in figure 1. Solve for the three currents, I1,I2,I3. 2. Relevant equations KVL: Sum of voltages in a closed loop equals zero KCL: Sum of currents entering a junction equals the sum of currents exiting a junction Ohm's Law: V=IR NOTE: Nodal analysis is not allowed for this solution 3. The attempt at a solution Through KCL, calling I5 the current leaving the junction on the left-hand side of the circuit and I4 the current leaving the junction on the right-hand side of the circuit: I2=I5+I3 I4=I3+I1 Then... the KVL equations for each loop: 5I5-10I3-8I4=0 5I5-12+I2=0 8I4-9+I1=0 -I2+12-10I3-9+I1=0 -I2+12-5I5+8I4-9+I1=0 -10I3-9+I1+5I5=0 -10I3-8I4-I2+12=0 Okay...so I can't come up with a methodical way of plugging these equations into one another and solving for any unknowns. It just seems...honestly impossible. We haven't learned any clever tricks involving ignoring one battery (I've seen that in solutions elsewhere), and when the professor mentioned this question he presented it as pretty straightforward...is there something major that I'm missing? I feel like I have a firm grasp of the mathematics and physics involved but I still can't produce any sort of solution. When I have I've found a mistake somewhere in my math.