We will start with this verse which speaks of Jesus, from the book of Isaiah.
Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. Isaiah 53:10-11 (KJV - emphasis added)
In the New Testament we read much about how God's righteous servant, Jesus, justifies us (that is, he reconciles us with God). In the verse below, the Apostle Paul is saying what the purpose of the law is:
Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin. Romans (KJV)
We see, then, that the law cannot justify, but rather shows us that we are indeed sinners. Here is another verse to that effect.
What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet. But sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead. Romans 7:7-8 (KJV)
The law cannot justify, but Jesus can.
Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified. Gal (KJV - emphasis added)
The following verses are from the Romans 3 discourse on justification. These verses tie together the law, the prophets, Jesus, and justification much better than I can!
But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: For all have sinned, and come short of the glory of God; Being justified freely by his grace through the redemption that is in Christ Jesus: Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus. Romans 3:21-26 (KJV - emphasis added)
Therefore we conclude that a man is justified by faith without the deeds of the law. Romans (KJV)
These verses have plainly showed that justification comes through Jesus, but how?
Jesus’ death on the cross was the last bloody sacrifice that God requires for the penalty of our sins.
But Christ being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building; Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption for us. For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? Heb 9:11-14 (KJV)
Later the author of Hebrews says of Jesus’ sacrificial death on the cross:
And 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. Heb 10:11-14 (KJV - emphasis added)
That passage continues to speak of the covenant God has made with them who believe in the sacrifice of Jesus.
Whereof the Holy Ghost also is a witness to us: for after that he had said before, This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; And their sins and iniquities will I remember no more. Heb 10:15-17 (KJV)
Also, consider these words from Peter:
For even hereunto were ye called: because Christ also suffered for us, leaving us an example, that ye should follow his steps: Who did no sin, neither was guile found in his mouth: Who, when he was reviled, reviled not again; when he suffered, he threatened not; but committed himself to him that judgeth righteously: Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed. For ye were as sheep going astray; but are now returned unto the Shepherd and Bishop of your souls. 1 Peter 2:21-25 (KJV)
These last two verses also come from Peter:
Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; But with the precious blood of Christ, as of a lamb without blemish and without spot:
1 Peter 1:18-19 (KJV)
Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever. 1 Peter 1:23 (KJV)
God has sent His Son, Jesus, to die on the cross – as the punishment for our sins. Jesus is the key to salvation, friends. You must believe that Jesus was perfect, that He died on the cross, and rose from the dead. You must believe that you cannot earn salvation on your own.
Jesus took all your sins upon Himself, so that you can appear before God as spotless. You see – He took our sins, and we took His righteousness before God.