2 different lineages

Matt. was written specifically to the Jews. Matthew was written to prove that Jesus was the messiah and the king of the Jews, because the Jews require a sign.

There is a thread in Scripture and Doctrine which answers this question more fully in a post by Hulsey.

Basically, the lineage of both Mary and Joseph is covered by these two genealogies, confirming that Jesus is the Messiah for whom Israel waited.