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Hebrews, chapter 10 is a good place to find the answer to your question.  The reason that there were continuing sacrifices under that law was because these sacrifices could never take away the sins of those who offered them.  Let’s read Hebrews 10:1-4, “For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.  But in those sacrifices there is a remembrance again made of sins every year. For it is not possible that the blood of bulls and of goats should take away sins.”  We learn from this that the keeping of the law and the sacrifices that were made were never intended to take away sin.  They were “a shadow of good things to come.”  They were types of the Lord Jesus Christ Himself, who would one day give Himself as the perfect sacrifice to God to put away our sins forever.  The continuing sacrifices could not do away with sins; they only acted as reminders of the sins of the people.  If the sacrifice had put away their sins, they would have ceased making the sacrifices.

Let’s continue by reading Hebrews 10:5-10, “Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me:  In burnt offerings and sacrifices for sin thou hast had no pleasure. Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God. Above when he said, Sacrifice and offering and burnt offerings and offering for sin thou wouldest not, neither hadst pleasure therein; which are offered by the law; Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second. By the which will we are sanctified through the offering of the body of Jesus Christ once for all.”  The Lord Jesus came into the world to do His father’s will, and that was to give Himself for us as the one perfect sacrifice that pleased God to the putting away of our sins.  As we read in verse 10, “we are sanctified through the offering of the body of Jesus Christ once for all.”

We read in Hebrews 10:11-14 that, “…every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins: But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God; From henceforth expecting till his enemies be made his footstool. For by one offering he hath perfected for ever them that are sanctified.”  What a powerful sacrifice!  The offering of the Lord Jesus has sanctified us and perfected us forever.  There is no more work to be done to accomplish salvation.  Christ was able to sit down on the right hand of God because He had put away our sins forever.  The work was over.  Listen to the words of the Lord Jesus as He cries from the cross in John 19:30, “When Jesus therefore had received the vinegar, he said, It is finished: and he bowed his head, and gave up the ghost.”  “It is finished.”  What an incredible statement.  It’s over!  The atoning work was completed.  In the Greek, “It is finished” is just one word, ‘teleo’.  The definition of this word is: PAID.  The Lord’s cry from the cross assures us that the debt of our sins has been paid in full.

Let’s read Hebrews 9:24-28, “For Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us: Nor yet that he should offer himself often, as the high priest entereth into the holy place every year with blood of others; For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself. And as it is appointed unto men once to die, but after this the judgment: So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation.”  Christ died once.  He was offered once to bear the sins of many.  Once was enough.  God was satisfied with the sacrifice of His son.  There is no more a remembrance for sin to those who believe on the Lord Jesus Christ.  We rest in His finished work.