Why do Matthew and Luke give different genealogies of Jesus?

Matthew 1:1–17

¹The book of the generation of Jesus Christ, the son of David, the son of Abraham. ²Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas and his brethren; ³And Judas begat Phares and Zara of Thamar; and Phares begat Esrom; and Esrom begat Aram; ⁴And Aram begat Aminadab; and Aminadab begat Naasson; and Naasson begat Salmon; ⁵And Salmon begat Booz of Rachab; and Booz begat Obed of Ruth; and Obed begat Jesse; ⁶And Jesse begat David the king; and David the king begat Solomon of her that had been the wife of Urias; ⁷And Solomon begat Roboam; and Roboam begat Abia; and Abia begat Asa; ⁸And Asa begat Josaphat; and Josaphat begat Joram; and Joram begat Ozias; ⁹And Ozias begat Joatham; and Joatham begat Achaz; and Achaz begat Ezekias; ¹⁰And Ezekias begat Manasses; and Manasses begat Amon; and Amon begat Josias; ¹¹And Josias begat Jechonias and his brethren, about the time they were carried away to Babylon: ¹²And after they were brought to Babylon, Jechonias begat Salathiel; and Salathiel begat Zorobabel; ¹³And Zorobabel begat Abiud; and Abiud begat Eliakim; and Eliakim begat Azor; ¹⁴And Azor begat Sadoc; and Sadoc begat Achim; and Achim begat Eliud; ¹⁵And Eliud begat Eleazar; and Eleazar begat Matthan; and Matthan begat Jacob; ¹⁶And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ. ¹⁷So all the generations from Abraham to David are fourteen generations; and from David until the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon unto Christ are fourteen generations.

Luke 3:23–38

²³And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli, ²⁴Which was the son of Matthat, which was the son of Levi, which was the son of Melchi, which was the son of Janna, which was the son of Joseph, ²⁵Which was the son of Mattathias, which was the son of Amos, which was the son of Naum, which was the son of Esli, which was the son of Nagge, ²⁶Which was the son of Maath, which was the son of Mattathias, which was the son of Semei, which was the son of Joseph, which was the son of Juda, ²⁷Which was the son of Joanna, which was the son of Rhesa, which was the son of Zorobabel, which was the son of Salathiel, which was the son of Neri, ²⁸Which was the son of Melchi, which was the son of Addi, which was the son of Cosam, which was the son of Elmodam, which was the son of Er, ²⁹Which was the son of Jose, which was the son of Eliezer, which was the son of Jorim, which was the son of Matthat, which was the son of Levi, ³⁰Which was the son of Simeon, which was the son of Juda, which was the son of Joseph, which was the son of Jonan, which was the son of Eliakim, ³¹Which was the son of Melea, which was the son of Menan, which was the son of Mattatha, which was the son of Nathan, which was the son of David, ³²Which was the son of Jesse, which was the son of Obed, which was the son of Booz, which was the son of Salmon, which was the son of Naasson, ³³Which was the son of Aminadab, which was the son of Aram, which was the son of Esrom, which was the son of Phares, which was the son of Juda, ³⁴Which was the son of Jacob, which was the son of Isaac, which was the son of Abraham, which was the son of Thara, which was the son of Nachor, ³⁵Which was the son of Saruch, which was the son of Ragau, which was the son of Phalec, which was the son of Heber, which was the son of Sala, ³⁶Which was the son of Cainan, which was the son of Arphaxad, which was the son of Sem, which was the son of Noe, which was the son of Lamech, ³⁷Which was the son of Mathusala, which was the son of Enoch, which was the son of Jared, which was the son of Maleleel, which was the son of Cainan, ³⁸Which was the son of Enos, which was the son of Seth, which was the son of Adam, which was the son of God.