Legend:

• The 2nd is through Mary's line
  
  
• This is an error

Discussion:

• The first genealogy in Matthew is through Joseph. The one in Luke is for Mary
  
  
  • How do we know This?
    
    
    • One clue is that the genealogy states Jesus was "supposedly the son of Joseph". (Luke 3:23). This indicates it is not necessarily a biological record.
      
      
    • Also Matthew was writing to the Jews who were only concerned with the legal lineage. Luke, a physician, was not writing to the jews and would most likely of shown the biological lineage.
      
      
    • The early church would have know about this blatant difference and had no problem with it. They understood there was not contradiction
      
      
    • It was customary to list the genealogy through the father. Notice in Luke we are starting with Jesus and going backwards. We are not actually starting with Mary just going through her linage. Because only the names of fathers are listed, it would make sense to list Mary under her husbands name (the headship).
      
      
  • Why do we need Mary's when we have Joseph's. His would have been more accepted as it was customary to go through the father.
    
    
    • In Joseph's genealogy there is a man name Jeconiah. God cursed Jeconiah, saying that none of his descendants would ever sit on throne of David. (Jer 22:30) However, Jesus would sit on the throne. We show through Mary's line that he is not a biological descendant of Jeconiah, but has the legal rights through Joseph's.