# Solution of Linear Electrical Circuit

We learned in class that the number of independent KCL equations is N-1(N-number of nodes) and the number of independent KVL equations is B-(N-1) (B- number of branches). Thus we have B independent equations and we can solve the circuit for the currents. What I don't understand is how can we know for sure that the B equations are independent? The union of two independent sets of vectors is not necessarily also independent.