We have studied the thermodynamic properties of the ammonium nitrate/ammonium sulfate/water system using differential scanning calorimetry And infrared spectroscopy of thin films at low temperatures. This is the first study focused on low temperatures, as previous experimental work on this system has been at 273 K and above. We have combined our experimental results with melting point data from the literature at high temperatures to create a solid/liquid phase diagram of the ammonium nitrate/ammonium sulfate/water system for temperatures below 343 K. Using phase diagram theory and Alkemade lines, we predict which solids are stable at equilibrium for all concentrations within the studied region. We also observed the decomposition of a solid at low temperatures which has not previously been reported. Finally, we have compared our predicted solids and final melting temperatures to the Aerosol Inorganics Model (AIM).