Kaiser Permanente officials issued a statement confirming the couple had worked at their hospital in West Los Angeles but would not say when they had lost their jobs or provide other details. “We are deeply saddened to hear of the deaths of the Lupoe family,” the statement said.

Although the police are treating the case as a murder-suicide, Deputy Chief Kenneth Garner said the police were still sorting through a discrepancy.

Contrary to his fax and reported call to the television station, the man told a 911 operator he had arrived home and found his family dead, Deputy Chief Garner said. But investigators found a revolver next to Mr. Lupoe’s body, the only weapon in the home, he said.

The police said they found the bodies of the three daughters next to their father in a front bedroom upstairs. The boys were with their mother in a back bedroom on the same floor.

“A man who recently lost his job allowed the despair to put him over the edge,” said Mayor Antonio Villaraigosa, who held a news conference outside the house. “Unfortunately, this has been an all-too-common story in the last few months. But that does not and should not lead people to resort to desperate measures.”

A man killed his ex-wife, her parents and friends at a Christmas party in West Covina last month after losing his job. In October, a 45-year-old father of three shot and killed his wife and children in their Porter Ranch home after describing financial stress in a suicide note.

Mayor Villaraigosa urged Los Angeles residents experiencing financial stress to talk to friends and neighbors and seek counseling “to get back on their feet and keep their families afloat.”