There are direct links between water and energy use, sometimes referred to as the energy-water nexus. Water rights issues have confronted the southwestern U.S. for a long time. Furthermore, climate change is decreasing the already limited water resources in this region, and the growing population in the Southwest has also increased the consumption of freshwater. Here we study solar energy, which is abundant in the Southwest, as both an electric power source and the energy source to operate a desalination plant. We compare the use of different desalination technologies for seawater and brackish groundwater, which have different salinities. The data show that the dual-purpose reverse osmosis desalination plant is the most economical choice. However, since a multiple-effect desalination (MED) and a multistage-flash (MSF) can use waste heat for water production, desalinated water becomes a byproduct of the electric power plant, thus dual-purpose MED and MSF plants will be more economical than a single-purpose power plant. A MED plant using seawater or brackish water produces fresh water for $1.73/m3, while the costs are $2.811m3 and $2.65/m3 for a MSF plant using seawater and brackish water, respectively.