The four Southwestern state of the US that are all on the border of Mexico are Texas, California, New Mexico and Arizona. From West to East they would be; California, Arizona, New Mexico and Texas.
Depending on how you define Southwestern states, you have Arizona and New Mexico for certain. California and Texas can be added to your list if your definition is broad enough. All of these states border Mexico. None of the states on the Canadian border would be considered "southwetern".
Mexico borders the Southwestern states of Arizona, New Mexico and Texas.
It shares a common border with the Southwestern states of Texas, New Mexico, Arizona and California.
Southeastern
Montana does not border Mexico.
Arizona ("AZ") lies in the southwestern United States, on the border with Mexico.
Arizona lies in the southwestern United States, on the border with Mexico. The state is bordered by Utah to the north, by New Mexico to the east, to the south by the states of Sonora and Baja California (Mexico), and to the west by California and Nevada.
The state of New Mexico is located in the southwestern United States, along the U.S.-Mexico border. Mexico (the country) on the other hand, is along the southern boundary of the United States, bordering California, Arizona, New Mexico and Texas.
There are two of them; one is known as Sierra Madre del Sur and runs from southwestern Jalisco to the east of the state of Oaxaca; the other one is the Sierra de Chiapas which runs along that state weastward into the Mexico-Guatemala border.
If you mean NEW Mexico, it is a state located in the southwestern United States.
Last time it was modified was during the Gadsden Purchase, in 1853.