Does the New Testament quote from the Greek Septuagint?

The KJV Old Testament is translated from the Ben Chayyim Masoretic text of the Hebrew scriptures.  Some translations such as the NIV and ESV depart from the Hebrew scriptures in a number of places (e.g. Genesis 47:21, Genesis 49:10, Judges 14:15, Judges 16:13-14, 1 Samuel 1:24, 2 Samuel 7:16, 2 Samuel 15:7, 2 Samuel 24:13).  Instead, these translations follow the ancient Greek translation of the Old Testament called the Septuagint (abbreviated as the LXX) which was allegedly made before the time of Christ.  These translators feel justified to follow the LXX because they believe that Jesus and the Apostles used the LXX instead of the Hebrew scriptures.  To try to prove their point, they often refer to Luke 4:18-19 where it is alleged to be an instance of Jesus quoting Isaiah 61:1-2 from the LXX instead of from the Hebrew scriptures.  Luke 4:18-19 in the KJV says,

“The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, To preach the acceptable year of the Lord.”

Compare the above with Isaiah 61:1-2 in the LXX as well as in the Hebrew scriptures:

LXX (Lancelot C. L. Brenton English translation of the LXX):
“The Spirit of the Lord is upon me, because he has anointed me; he has sent me to preach glad tidings to the poor, to heal the broken in heart, to proclaim liberty to the captives, and recovery of sight to the blind; to declare the acceptable year of the Lord”
Hebrew (as translated in the KJV):
“The Spirit of the Lord GOD is upon me; because the LORD hath anointed me to preach good tidings unto the meek; he hath sent me to bind up the brokenhearted, to proclaim liberty to the captives, and the opening of the prison to them that are bound; To proclaim the acceptable year of the LORD”

As seen in the comparison, it is simply not true that Luke 4:18 agrees more with the LXX than the Hebrew text.  The clause, “recovering of sight to the blind” in Luke 4:18 matches the clause, “recovery of sight to the blind” in Isaiah 61:1 in the LXX.  The Hebrew text does not explicitly mention the “blind.”  However, the Hebrew text has a clause that is not in the LXX.  The Hebrew text’s “the opening of the prison to them that are bound” matches Luke 4:18’s “to set at liberty them that are bruised” (“The opening of the prison” carries the same sense as “to set at liberty” and “bound (Strong’s H7533)” can be translated “bruised.”).

Another complication gets added for those who reject the Textus Receptus (the Greek New Testament text underlying the KJV) in preference for the Alexandrian Nestle-Aland text which underlies the New Testament of translations such as the NIV and ESV.  The LXX includes the clause, “to heal the broken in heart” at Isaiah 61:1, but the Alexandrian text of Luke 4:18 omits the clause.  Luke 4:18-19 in the ESV says:
ESV:
“The Spirit of the Lord is upon me, because he has anointed me to proclaim good news to the poor. [CLAUSE OMITTED] He has sent me to proclaim liberty to the captives and recovering of sight to the blind, to set at liberty those who are oppressed, to proclaim the year of the Lord’s favor.”
The omission is supported by the two earliest extant manuscripts, Codex Sinaiticus and Codex Vaticanus.  The inclusion of the clause is supported by the majority of manuscripts and the third earliest extant manuscript, Codex Alexandrinus (Nestle-Aland: Novum Testamentum Graece, 27th revised edition (2006)).  Thus if you believe that the “earliest manuscripts” are more reliable, then you will have a harder time claiming that Jesus quoted the LXX as Jesus in these Alexandrian manuscripts omits not just one but two clauses which appear in the LXX.

The fact of the matter is that Luke 4:18 matches neither the LXX nor the Hebrew text exactly.  The LXX has one clause that the Hebrew text does not have, but the Hebrew text has one clause that the LXX does not have.  So Luke 4:18 is not proof that Jesus quoted the LXX.  If you believe that Jesus quoted the LXX, you would still have to explain how Jesus got the one clause that is missing in the LXX.  Neither the LXX nor the Hebrew text matches Luke 4:18 exactly because Jesus was not quoting word for word from any text.  Rather, Jesus was expounding Isaiah 61:1 by providing his targum (a paraphrase).  New Testament scholar Craig A. Evans states as follows:

“Jesus cites in a synagogue (4:18-19) what appears to be a passage from Isaiah 61, but it turns out to be a mixture of several passages or themes from the book of Isaiah.  Among them is Isaiah 42, which in the Targum (42:3, 7) especially refers to the poor, the blind, and prisoners, who are pointedly mentioned in Jesus’ “citation.”” (Dr. Craig A. Evans, From prophecy to testament: the function of the Old Testament in the New).

Jesus incorporated Isaiah 42:7 into his reading of Isaiah 61:1 in order to provide a helpful cross-reference to the phrase, “opening of the prison to them that are bound” (Isaiah 61:1).  Isaiah 42:6-7 says, “I the LORD have called thee… to open the blind eyes, to bring out the prisoners from the prison, and them that sit in darkness out of the prison house.”  In Isaiah 42:7, Hebrew parallelism suggests that “open the blind eyes” is related to “bring out the prisoners from the prison.”  They both refer to a person coming out of spiritual darkness and bondage.  Thus Jesus read Isaiah 42:7 into Isaiah 61:1.  Well-studied fellow Jews in the Synagogue would have understood that Jesus was “cross-referencing” Isaiah 42:7 from Isaiah 61:1 because Isaiah 42:7 expands the meaning of “opening of the prison” in Isaiah 61:1.
Also, the Hebrew text’s Isaiah 61:1 has “GOD” (a translation of “יהוה”) in the first sentence after “Lord,” but Luke 4:18 omits it. The LXX Isaiah 61:1 also lacks “GOD.” This, however, does not mean that Jesus quoted the LXX.  In keeping with Jewish custom Jesus would not have uttered the Tetragrammaton (the sacred name of God) in the synagogue. The Hebrew text’s Isaiah 61:1 has “GOD” because it was in writing, but Luke 4:18 does not have “GOD” because Jesus’ utterance in a Synagogue would not have included it. The lack of “GOD” in Luke 4:18 has nothing to do with Jesus quoting the LXX.
Luke 4:18-19 is the most common Old Testament quotation that is attributed to the LXX, but it can also be attributed to the Hebrew text if we examine the passage a little more and consider Jewish custom.  As with this passage, other passages that are attributed to the LXX can also be explained without supposing the use of the LXX.  There is a lot of evidence that Jesus and the Apostles read and used the Hebrew Old Testament (he referred to “jots” and “tittles” and referred to the Old Testament in the Jewish order of books (Law, prophets, psalms)).