We report a study of displacement by xenon of a monolayer of sulphur hexafluoride initially condensed on a graphite surface. Earlier work showed that, below 112 K, Xe displaces SF6 almost completely in a first-order transition. Working at higher temperatures, we show that this system has a simple eutectic-like phase diagram, at least for SF6 not too dilute. In our experiment, both adsorbates are in equilibrium with their respective vapors in a cold cell. In our infrared reflection-absorption spectroscopy measurements, the SF6 coverage on the surface is monitored by the frequency shift due to dynamic dipole coupling of the collective mode of the strong SF6 ν3 vibrational resonance. Simulations relate this frequency shift to the SF6 areal density. Below T ≈ 134 K, with increasing Xe pressure, a small amount Xe dissolves in the solid SF6 monolayer preceding its displacement by a solid predominantly Xe monolayer in a first-order transition. Above 134 K, there is a weaker first-order transition to a mixed liquid monolayer, followed by continuous increase in Xe concentration. If the initial SF6 monolayer is near its melting line, the melting transition on adding Xe appears to become continuous.