The righteous will live by faith. (Habakkuk 2:4) This is perhaps the most important connection between two words in the Bible.
Righteousness and faith.
To be righteous means that you are right with God. You know what it feels like when your relationship with another person is just right. Nothing can stand between you, and you always do right by each other. With God, that’s called righteous, and in the Bible, it’s the only way to heaven.
“But those who depend on the law to make them right with God are under his curse, for the Scriptures say, ‘Cursed is everyone who does not observe and obey all the commands that are written in God’s Book of the Law.'” Galatians 3:10.
The problem is we can never live to the standard of righteousness set by God.
“So it is clear that no one can be made right with God by trying to keep the law…” Galatians 3:11.
So God made a way to reconcile us.
“But Christ has rescued us from the curse pronounced by the law. When he was hong on the cross, he took upon himself the curse for our wrongdoinge…” Galatians 3:13.
Jesus paid for our sins, to break the curse, and make us righteous. Right with God by faith in Jesus. The righteous shall live by faith.