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Maxwell Burke was the first officer of the USS Equinox, serving under Captain Rudolph Ransom. During his time at the academy, he had dated future Voyager officer B'Elanna Torres, who he nicknamed BLT before she dated Tom Paris and married him.
The Equinox was transported into the Delta Quadrant by the Caretaker in early 2371 some time before Voyager and faced a similarly long trip home. Early in the voyage, they suffered serious casualties in an encounter with the Krowtians, losing over half of the ship's already small crew. Low on resources, they began investigating a race of nucleogenic life-forms who could be summoned from subspace. After accidentally killing one by trapping it in a forcefield, they discovered the aliens' remains could be used for fuel and began deliberately killing them for this purpose, suffering reprisals in return.
When Voyager stumbled upon the Equinox, Ransom, Burke and the rest of the crew played the part of innocent victims of an unprovoked attack. Captain Janeway soon uncovered the truth and placed them under arrest but they escaped with the help of the Equinox EMH, stealing a shield module from Voyager and beaming back to the Equinox, before warping away and leaving Voyager under attack from the aliens.
While Burke was becoming increasingly blasé about what they were doing, thinking nothing of reporting they needed more alien corpses, Ransom's conscience began to trouble him and he made the choice to surrender to Voyager. However, Burke refused to let all their work be for nothing and mutinied, ordering Ransom confined to the brig. Chief engineer Marla Gilmore appeared to comply but instead took Ransom to Engineering, where they tried to regain control of the ship.
Voyager arrived on the scene but Burke had the Equinox EMH, who had been left on board, sabotage the ship, planning to destroy it. Torres personally contacted Burke to ask him to stand down but Burke remained unswerving, although he did express regret that she would be among those killed. However, the tide began to turn against him as the aliens attacked the ship, draining power and leaving only the bridge shielded. Ransom beamed all surviving crewmembers except himself and the bridge crew over to Voyager, where the EMH was soon exposed and deleted.
With the combined actions of Ransom, Voyager's crew and the aliens, the Equinox was soon damaged beyond the point of saving. Although his helmsman, Crewman Thompson, wanted to surrender to Voyager, Burke insisted on trying to escape via a shuttle. As his party headed to the shuttlebay, they were attacked by the aliens and all killed.
There is some confusion over Burke's rank. He wears lieutenant's pips, and is referred to as such in supplementary material, but is referred to as a commander in the story's dialogue.