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Hybrid dynamic systems combine advantages from different subsystems for realizing information processing tasks in both classical and quantum domains. However, the lack of controlling knobs in tuning system parameters becomes a severe challenge in developing scalable, versatile hybrid systems for useful applications. Here, we report an on-chip microwave photon–magnon hybrid system where the dissipation rates and the coupling cooperativity can be electrically influenced by the spin Hall effect. Through magnon–photon coupling, the linewidths of the resonator photon mode and the hybridized magnon polariton modes are effectively changed by the spin injection into the magnetic wires from an applied direct current, which exhibit different trends in samples with low and high coupling strengths. Moreover, the linewidth modification by the spin Hall effect shows strong dependence on the detuning of the two subsystems, in contrast to the classical behavior of a standalone magnonic device. Our results point to a direction of realizing tunable, on-chip, scalable magnon-based hybrid dynamic systems, where spintronic effects provide useful control mechanisms.