The traditional view is that Matthew was the first written Gospel and that Mark summarized that account for easier consumption. More recently, however, scholars find the case for Markian prioritythe case for Markian priority stronger and therefore Matthew was an expansion of Mark. When all three synoptics share text (the triple-tradition), Luke invariably follows the Mark reading rather than the Matthew reading. This strongly suggests that Luke did not actually have access to Matthew as one of his sources.
But the Farrer theory does not explain why or how Matthew and Luke could present contradictory evidence on key points of the story. What was Jesus'Jesus' genealogygenealogy? Who was at the tombWho was at the tomb when the women arrived? How many demon-possessed mendemon-possessed men or blind menblind men did Jesus heal? How did Judas die? Why does Luke provide his own birth narratives and resurrection appearances without referencing Matthew's different accounts?