How do we reconcile the 2 geneologies given to us in scripture?  We have....
 
Matt 1:16 And Yacov begat Yoseph the husband of Miriam,
                 of whom was born Yeshua, who is called Messiah.
 
"begat" would mean Yacov was Yoseph's natural father.  But in Luke we have...
 
Luke 3:23   And Yeshua himself began to be about thirty
                     years of age, being (as was supposed) the
                     son of Yoseph, who was the son of Heli,

 
Was Yeshua the natural son of Yoseph?  No.  Was Yoseph the natual son of Heli?  No.  Yeshua was the son of Yoseph by law, since he was raised by Yoseph, the husband of Yeshua's mother.
 
There's two possible explanations for this.  One, is that Luke is describing Miriam's line and her father was Heli.  Yoseph was his "son" [in-law] which is simply listed here as "son".  Possibility #2, is that Yoseph's natural father, Yacov died at an early age, and his mother re-married to Heli and thus he was Heli's legal son, much like Yeshua was Yoseph's legal son, but not natural son.  But yes, this is explainable.   This is only an "error" to those not smart enough to figure out how both could be true.
 
The traditional explanation in most seminaries is that Matthew is Mary's lineage, and Luke is Joseph's.  I would say it would have to be the other way around, and that Matthew is the geneology of Yoseph/Joseph while Luke is Miriam's (Mary's).  For one, Luke lists more generation for the same time period, and in the first century AD, women married younger than men.  Most typical first marriages were by men in their 20's marrying 13 year old women who had just turned old enough to marry for the first time.  Men were expected to work and make a living to support a wife before taking a wife.
 
In Mattiyahu/Matthew you have 1000 years between David and Yoseph with 26 generations meaning the average patriarch gave birth at age 38.  I had a daughter at 38!  In Luke's geneology you have 41 generations over that same 1000 years meaning the average matriarch in that line is giving birth at age 24.  So the folks in Luke's geneology are having babies much earlier in life than the people in Matthew's geneology.  Why?  Probably because Luke is really listing a matriarchy of women who gave birth to women, but listing them according to the names of their husbands.
 
Another piece of evidence is that in Matthew, it tells Joseph's story and how he reacted to the news he heard when he was told that Miriam was pregnant, but not by him.  Yet in Luke, we see Miriam's (Mary's) story being told, and how the angel appeared to her and it provides HER perspective on the virgin birth, while Matthew provides Yoseph's (Joseph's) persective on the virgin birth.
 
 
 
Shalom, Yoseph
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