The Jaynes-Cummings system is one of the most fundamental models of how light and matter interact. When driving the system with a coherent state (e.g. laser light), it is often assumed that whether the light couples through the cavity or atom plays an important role in determining the dynamics of the system and its emitted field. Here, we prove that the dynamics are identical in either case except for the offset of a trivial coherent state. In particular, our formalism allows for both steady-state and the treatment of any arbitrary multimode coherent state driving the system. Finally, the offset coherent state can be interferometrically canceled by appropriately homodyning the emitted light, which is especially important for nanocavity quantum electrodynamics where driving the atom is much more difficult than driving the cavity.In this work, we study the Jaynes-Cummings (JC) Hamiltonian driven by a coherent state. The JC system consists of a single bosonic mode (e.g. an electromagnetic cavity) coherently interacting with a single fermionic mode (e.g. an electron or two-level atom). These modes are radiatively coupled to external reservoirs, which can cause the system to both leak or absorb energy depending on their state. Preparing the reservoirs with coherent light is one of the most common ways of pumping energy into the system, and provides an excellent way to understand its quantum-mechanical responses. Despite the simplicity of the JC model itself (Fig. 1), it gives rise to a variety of complex phenomena when driven. For example, vacuum Rabi splitting [1, 2], photon blockade [3-5] and tunneling [6], bistability [7, 8] or symmetry breaking [9], squeezed states [10], Mollow triplets [11] or state dressing [12], and a rich structure of multi-photon resonances [13,14] have all been observed, as well as finding use in the readout of qubits [15,16]. There are multiple ways to drive the JC system, as shown in Fig. 1. In particular, the coherent state could be prepared in the reservoirs coupled to the cavity or coupled to the atom [17]. Almost all of the above studies have shown substantive differences in observed radiation from FIG. 1. Schematic of a Jaynes-Cummings system, containing a two-level quantum system coherently interacting with a cavity mode. The cavity couples to the reservoir b, while the two-level atom couples to reservoir c. † These authors contributed equally.