Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins s₁ and s₂ on one- and two-dimensional lattices. The combined effect appears most visibly in the elementary excitation spectra. In contrast to the ground-state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The excitation modes also exhibit softening beyond a threshold value of frustration, signalling a transition from a classical ferrimagnetic state to a spiral state. The threshold value of frustration in a chain decreases with dimerization, showing that dimerization further assists in the phase transition. That the long-range classical ferrimagnetic order is destroyed is shown by the correlation length as well as sublattice magnetization decreasing with both dimerization and frustration. These effects have also been studied for a square lattice taking the dimerization interaction as J/(1∓δ) rather than J(1±δ) where the linear spin-wave theory shows that dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition.