If you read both articles explaining The Law of Moses versus Grace, then it should make sense why Christians are not to be living by the Law of Moses. But anyone that wants to be sure about their doctrine needs to read it for themselves in the Word of God. This article references the scriptures that provide the evidence of Christians not living under the Law. The book of Romans is a great book to read in gaining understanding of this point.
For sin shall not have dominion over you, for you are not under law but under grace. (Romans 6:14 NKJV)
But now we have been delivered from the law, having died to what we were held by, so that we should serve in the newness of the Spirit and not in the oldness of the letter. (Romans 7:6 NKJV)
What shall we say then? Is the law sin? Certainly not! On the contrary, I would not have known sin except through the law. For I would not have known covetousness unless the law had said, “You shall not covet.” (Romans 7:7 NKJV)
For Christ is the end of the law for righteousness to everyone who believes. (Romans 10:4 NKJV)
For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast. (Ephesians 2:8, 9 NKJV)
But if you are led by the Spirit, you are not under the law. (Galatians 5:18 NKJV)
For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him. For “whoever calls on the name of the LORD shall be saved.” (Romans 10:12, 13 NKJV)
for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, (Romans 2:14 NKJV)
For whoever shall keep the whole law, and yet stumble in one point, he is guilty of all. (James 2:10 NKJV)
But we know that the law is good if one uses it lawfully, knowing this: that the law is not made for a righteous person, but for the lawless and insubordinate, for the ungodly and for sinners, for the unholy and profane, for murderers of fathers and murderers of mothers, for manslayers, for fornicators, for sodomites, for kidnappers, for liars, for perjurers, and if there is any other thing that is contrary to sound doctrine, (I Timothy 1:8-10 NKJV)