Romans 4:16-17

¹⁶ “For this reason it is by faith, in order that it may be in accordance with grace, so that the promise will be guaranteed to all the descendants, not only to those who are of the law, but also to those who are of the faith of Abraham, who is the father of us all, ¹⁷ (as it is written: “I have made you a father of many nations”) in the presence of Him whom he believed, that is, God, who gives life to the dead and calls into being things that do not exist.

Here we see the reason why righteousness is a free gift given when we believe. God has the system rigged so that nothing depends on our works. This allows Him to save us completely. So, Jews, who have the law, are saved apart from the law through faith. Gentiles, who never had the written law, are also saved through faith apart from the law. 

Life to the dead: Here we see the other half of the Gospel. Not only are Christians righteous in the sense that we are forgiven, but God gives eternal life to all who believe. God does not just save us and wish us luck on the Christian life: Paul is presenting a much more complete Gospel than this.