Note 1 at Lk. 3:23: The genealogy in Matthew is from Abraham to Jesus while Luke traces Jesus' ancestry from Jesus all the way back to Adam. The genealogies are the same from Abraham to David, but from David to Jesus, they are totally different. Both these genealogies were accepted by the early church despite their differences, which is proof enough of their accuracy.

The answer appears to be that Matthew traces David's line through Solomon (Mt. 1:6), while Luke traces the royal lineage through Nathan, another son of David (Lk. 3:31; 2 Sam. 5:14). This would by-pass the curse on Jechonias' seed listed in Jeremiah 22:24-30 (see ref. bb at Mt. 1:1, p. 4).

The justification for two genealogies is that Matthew records Joseph's line while Luke records Mary's line. Luke does say Joseph was the son of Heli, which would appear that Luke is also tracing Joseph's lineage, but that would not have to be the case. There is scriptural precedent for a man's first son to be reckoned to the mother's genealogy if her father had no sons (Num. 27:1-11 and 36:1-12 with Ruth 4:6). This could explain the substitution of Joseph's name for Mary's in Luke's account. This is especially appropriate since Jesus was the seed of the woman (Gen. 3:15), not the seed of man.