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The rapid progress in quantum-optical experiments especially in the field of cavity quantum electrodynamics and nanoplasmonics, allows to substantially modify and control chemical and physical properties of atoms, molecules and solids by strongly coupling to the quantized field. Alongside such experimental advances has been the recent development of ab-initio approaches such as quantum electrodynamical density-functional theory (QEDFT) that is capable of describing these strongly coupled systems from first-principles. To investigate response properties of relatively large systems coupled to a wide range of photon modes, ab-initio methods that scale well with system size become relevant. In light of this, we extend the linear-response Sternheimer approach within the framework of QEDFT to efficiently compute excited-state properties of strongly coupled light-matter systems. Using this method, we capture features of strong light-matter coupling both in the dispersion and absorption properties of a molecular system strongly coupled to the modes of a cavity. We exemplify the efficiency of the Sternheimer approach by coupling the matter system to the continuum of an electromagnetic field. We observe changes in the spectral features of the coupled system as Lorentzian line shapes turn into Fano resonances when the molecule interacts strongly with the continuum of modes. This work provides an alternative approach for computing efficiently excited-state properties of large molecular systems interacting with the quantized electromagnetic field.