Hab 2:4, Rom 3:20-21, Rom 9:30-33, Phil 3:9, Gal 3:11, Heb 10:38
In the Old Testament, it was prophesied that the righteous would live by faith. (Hab 2:4)
Hab 2:4 Behold, his soul which is lifted up is not upright in him: but the just shall live by his faith.
The law convicts us of sin. In addition to the law, the righteousness of God has been revealed, and it is the Christ of which the law and the prophets testified. (Rom 3:20-21)
Rom 3:20 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. 21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
We are justified by God by believing that Jesus is the Christ. (Rom 1:17, Phil 3:9, Gal 3:11, Heb 10:38, Rom 9:30-33)
Rom 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
Phil 3:9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:
Gal 3:11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith.
Heb 10:38 Now the just shall live by faith: but if any man draw back, my soul shall have no pleasure in him.
Rom 9:30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith. 31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. 32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone; 33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.