After his lawyers could not persuade the USA's most important court to delay his punishment, Elliott was killed by a special injection, called a lethal injection.
In some parts of the US, the death penalty is the harshest punishment for such serious crimes.
The state of Texas executes more of its prisoners than anywhere else in the US. The UK got rid of the death penalty for murder in 1965.
His family prayed aloud
Jackie Elliott's sister and other members of his family came to the prison and said prayers as he died.
He was pronounced dead seven minutes after the lethal injection started.
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