To live by faith is to live in righteousness. It is not possible to have faith in the Truth and live in Lies. It is not possible to believe in the Word of God and do what pleases the devil unless this faith is religious or emotional.
But when faith is founded on the Word of the Wisdom of God and practiced in an intelligent way, it is impossible for this faith to fail.
The Lord Jesus Christ is the Author and Finisher of the Intelligent Faith, this is, He is the Creator and Finisher of the Faith. This is why faith and righteousness are inseparable; they walk together. Faith typifies man with the image of God, and Righteousness, the Holy God of Saints.
And isn’t this what the LORD teaches when He says:
But the righteous one will live by his faith. Habakkuk 2.4 HCSB
But My righteous one will live by faith; and if he draws back, I have no pleasure in him. Hebrews 10.38 HCSB
This shows the eternal marriage of faith and righteousness. Faith justifies the sinner.
To live by faith is to live by what is righteous, honest, correct, praiseworthy, and pleasing before the Most Holy Righteous God. God is Righteous and lent us Faith so that we may live a righteous life and in communion with Him. This is, from faith to faith or righteousness to righteousness. This kind of faith is what pleases God.