If this magazine were about ten pages longer, perhaps. Of the places where the New Testament quotes the Old, the great majority is from the Septuagint version. Protestant authors Archer and Chirichigno list 340 places where the New Testament cites the Septuagint but only 33 places where it cites from the Masoretic Text rather than the Septuagint (G. Archer and G. C. Chirichigno, Old Testament Quotations in the New Testament: A Complete Survey, 25-32).
For those who may not know, the Septuagint was the Greek translation of the Hebrew Old Testament. The common abbreviation for it—LXX, or the Roman numerals for 70—come from a legend that the first part of the Septuagint was done by 70 translators.
By the first century, the LXX was the Bible of Greek-speaking Jews and so was the most frequently used version of the Old Testament in the early Church. For this reason, it was natural for the authors of the New Testament to lift quotes from it while writing in Greek to the Church.
But, while the New Testament authors quoted the LXX frequently, it does not necessarily follow that Christ did. We know for certain that Jesus quoted the Hebrew Old Testament at times, since he read from the scrolls in the synagogue. But Jesus could have only quoted from the Hebrew, and the New Testament authors later used the Greek translation to record the fact.
Either way, it doesn’t matter, because the Greek New Testament is inspired, and the Holy Spirit chose to have the sacred authors repeatedly cite the LXX. It doesn’t really matter if Jesus was quoting Scripture in Hebrew or Aramaic if the Holy Spirit chooses to use the Septuagint when translating his words into Greek. The importance of the Septuagint is demonstrated no matter which of these is the case.
But, since you ask, here is an example where the Greek gospels present Jesus as quoting the Septuagint: In Mark 7:6–7, Jesus quotes the LXX of Isaiah 29:13 when he says, “Well did Isaiah prophesy of you hypocrites, as it is written, ‘This people honors me with their lips, but their heart is far from me; in vain do they worship me, teaching as doctrines the precepts of men.’”
Of course, the reason people usually ask about the New Testament authors’ use of the Septuagint is because it contains the seven deuterocanonical books that are now omitted from Protestant Bibles. Showing that the New Testament authors quoted from the LXX argues in favor of (though does not in itself prove) the inspiration of these seven books.
For a full list of potential New Testament allusions to the deuterocanonical books, refer to this list compiled by Jimmy Akin.