"The just shall live by faith" (Romans 1:17).
The "just" to whom the Apostle Paul refers are literally the "justified." "Therefore being justified by faith, we have peace with God through our Lord Jesus Christ" (Romans 5:1). No human being is capable of making himself just before the God whose "way is perfect" (II Samuel 22:31). If born as an offspring of sinful Adam's race, and if ever we have sinned, all hope for justifying ourselves must be abandoned in the awareness that, by definition, a perfect Lord requires perfect righteousness. This He provides as a free gift to all who trust in the Christ whereby we are "accepted in the Beloved" (Ephesians 1:6).
Those justified by faith also live by faith. That is, we live by the confession and belief that Jesus is the Christ, and by the subsequent acknowledgement that all we are and all we have belongs to the Lord who is also our life. Authentic Biblical faith involves the confidence of the trust that rests in Christ, and the presentation of ourselves to Him "as those which are alive from the dead" (Romans 6:13). We live "looking unto Jesus the author and finisher of our faith," and also affirming that "ye are not your own, for ye are bought with a price" (Hebrews 12:2; I Corinthians 6:19-20).
This dual expression of rest and submission establishes the life by faith that leads to consistent bearing of the fruit of the Spirit. Indeed, born again believers do not live by prayer, but by the faith that leads to prayer. We do not live by obedience, but by the faith that leads to obedience. We do not live by self sacrifice, but by the faith that leads to self sacrifice. And we do not live by dedication and discipline, but by the faith that leads to dedication and discipline. We live by the God-given light that reveals the person and work of Christ, and by the trusting response of confidence and submission as enabled by the indwelling Holy Spirit. "So then faith cometh by hearing, and hearing by the Word of God" (Romans 10:13).
The reception of a free gift by faith births a new person who lives by faith. This "new man" is "created in righteousness and true holiness" (Ephesians 4:24). He rejoices in being freely justified and in belonging to Another. Thereby he lives, or rather Christ lives in him that he may live by Christ (Galatians 2:20). Yes, the justified live by the faith that affirms the peace of both confidence in God and consecration to God.
"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."