Figure 7.8 shows the two LTI systems having common input x(n). Their outputs are y1(n) and y2(n) respectively which are added to get the net output y(n). The systems are in parallel mode.
Fig. 7.8 Replacement of parallel systems
Therefore, the parallel system can be replaced by a single system with impulse response [h1(n) + h2(n)].
Figure 7.9 shows the two systems which are in cascade i.e., in series.
Fig. 7.9 Replacement of cascade systems ...