It is a mistake in interpretation to look upon the Law of Moses as a decree of God that could (or would) save a person. Note what Paul said in Romans 8:3, “For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh” (ESV).
Pay particular attention to the commas, and remove the phrase between the commas and then read what is said: “For God has done what the law could not do.” Why could not the Law of Moses save? Because it was not designed to save anyone (cf. Acts 13:39), but to point out something the Lord wanted man to know: there is such a thing as sin, and it is damning! In the early stages of man’s existence, this concept was not unfamiliar, but now with a law in place, the Lord removed what excuse man was prone to make (Romans 3:19-20).
Thus, the Jew who tried to gain justification with God via the Law of Moses could not do so because the law brought to man’s knowledge his inability to hit “God’s mark” (sin means to miss the mark). Not only that, however, but in order to help man hit the mark, the Lord declared what kind of response man was to give, and He used Abraham to illustrate the point: faith. Note what Paul said, “but that Israel who pursued a law that would lead to righteousness did not succeed in reaching that law. Why? Because they did not pursue it by faith, but as if it were based on works” (Romans 9:31-32, ESV). In other words, they used their perceived “obedience” (or compliance) to the God’s (or the Law’s) demands as “work” to be done, and then “payment” to be made by the one who made the demand. Consequently, they thought, God “owed” them wages for that which they did, and this, they believed, was salvation.
The Law of Moses had a purpose, and that purpose included bringing the Savior into this world (Galatians 3:13-16, 19-27; 4:4). Thus, no one could be saved by the Law of Moses, even if lived perfectly. Those who tried, failed; they failed because, among other things, they failed to understand its purpose.