In order to predict the behavior of C_A2, we are required to model both tanks.  The component balance for A in the second reactor gives the desired output, but in terms of the input C_A1, which is an intermediate variable.   The component balance on the first reactor gives the intermediate variable C_A1 in terms of the input variable, C_A0.  These two equations can be combined to yield the desired input-output model.  The overall system is second order, and without two equations the model would be under-specified.