Michigan ? A teenager shot his former girlfriend four times outside her high school, then killed himself in one of two fatal U.S. school shootings Wednesday, authorities said.

Jessica Forsyth, 17, was taken to Hurley Medical Center in Flint, where she was upgraded Wednesday evening to fair condition, hospital spokeswoman Christie White said.

Midland Police Chief James St. Louis said the gunman, identified as David Turner, 17, of nearby Coleman, died in the parking lot.

Turner had gone to H.H. Dow High School on Wednesday morning to try to talk to Jessica, but he was turned away by school officials, the police chief said. The boy then called her and asked her to meet him outside the building.

After a conversation in the parking lot, Turner pulled a gun out of a backpack and shot her four times before turning the gun on himself, St. Louis said.

In Greenville, Texas, a 16-year-old student fatally shot himself inside the band hall at Greenville High School, police said.

Police responded to the shooting about 15 minutes before the first bell, and the student was pronounced dead later at a hospital, Greenville city spokeswoman Lori Philyaw said in a statement.