Albert Barnes Commentary Galatians 3:11

"Now that no man is justified by the law before God, is evident: for, The righteous shall live by faith;" — Galatians 3:11 (ASV)

But that no man is justified, etc. Paul proceeds to confirm the argument he has been pursuing with an express declaration from the Bible. The argument is this: "It is impossible that a person should be justified by the law, because God has appointed another way of justification." But there cannot be two ways of obtaining life; and since God has appointed faith as the condition on which people shall live, He has precluded them from the possibility of obtaining salvation in any other way.

For, The just shall live by faith. This is quoted from Habakkuk 2:4. This passage is also quoted by Paul in Romans 1:17. (See the notes on Romans 1:17).

The meaning here is that life is promised to a person only in connection with faith. It is not by the works of the law that this is accomplished. The condition of life is faith; and the one who believes, lives. The meaning is not, I understand, that the person who is justified by faith shall live; rather, it is that life is promised and exists only in connection with faith, and that the just or righteous person obtains it only in this way. Of course, it cannot be obtained by observance of the law, but must be by some other plan.