From a hermeneutical and grammatical exegesis of Romans 11:6And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then it is no more grace: otherwise work is no more work.
See All... And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work. It would be required to believe that works were necessary for salvation; and now they are not. Also, note the companion verse Romans 3:21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
See All... But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; If it is no more of works and now you get righteousness without the law, then isn't it clear that it used to be of works and used to be by the law?

I used to teach this verse as simply making a logical argument that grace and works could not both be causes for salvation. They were mutually exclusive as causes. If salvation was by one, then it could not be by the other.

I still believe that this verse teaches this. However, a further study of the context has convinced me that there is a historical element to the "no more of works" phrase. Romans 11:1I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.
See All... declares the principle that God has not cast away His people, the Jews. Romans 11:2-4 [2] God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel saying, [3] Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life. [4] But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.
See All... gives the example of the time that Elijah thought he was the only true believer left in Israel when there were 7,000 who had not bowed to Baal. Romans 11:5Even so then at this present time also there is a remnant according to the election of grace.
See All... assures the Romans that "at this present time also there is a remnant according to the election of grace." Then, Romans 11:6And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then it is no more grace: otherwise work is no more work.
See All... declares that the present remnant survives "no more of works," but now comes by grace.

The problem in interpretation comes because some Bible teachers assume that the comparison is of ways to receive eternal salvation. Although salvation is certainly included in those who are presently in the remnant according to grace, this is not the theme of this passage. The passage specifically refers to the preservation of a remnant among God's chosen earthly people--the Jews. Under the law, which was definitely a covenant of works, they maintained their status as the people of God by their works. In this age, they can truly be the people of God only by the election of grace--that is, by eternal salvation.

However, since the Bible is clear that the keeping of the law could save no one (Acts 13:39And by him all that believe are justified from all things, from which ye could not be justified by the law of Moses.
See All...; Romans 3:20Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.
See All...; Galatians 3:21-22 [21] Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law. [22] But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe.
See All...; Hebrews 7:11If therefore perfection were by the Levitical priesthood, (for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?
See All..., 19; 9:9
See All...), being part of the Old Testament Jewish remnant was not identical with eternal salvation. The text deals with being God's earthly people. In the Old Testament, this was maintained by the works of the law. In the New Testament, it is obtained by the election of grace through Jesus Christ. However, in the Old Testament, being God's faithful earthly remnant was not identical with having eternal salvation. Certainly, there were Gentiles who knew God as personal Saviour who were not a part of the Jewish remnant. Also, there were probably Jews who did not bow to Baal who had never truly believed in God as Saviour.

Romans 11:1-6 [1] I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin. [2] God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel saying, [3] Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life. [4] But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal. [5] Even so then at this present time also there is a remnant according to the election of grace. [6] And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then it is no more grace: otherwise work is no more work.
See All... does indicate a chronological difference, but it is a difference in how God preserved His remnant among the children of Israel. It was not a difference in how people went to heaven.

You also mention Romans 3:21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
See All..., which states, "But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets." There was a "righteousness of the law" (Romans 2:26Therefore if the uncircumcision keep the righteousness of the law, shall not his uncircumcision be counted for circumcision?
See All...) that was the result of keeping the law. Yet, however praiseworthy this righteousness was, it was not equivalent to eternal salvation. In fact, a legalistic keeping of the law was not a way to salvation.

Romans 9:31-32 [31] But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. [32] Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
See All... states, "But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone." Here we see that faith was the key to true righteousness even under the law. External righteousness could be maintained without a true internal salvation. Those who tried to establish their own righteousness through the law (Romans 10:3For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God.
See All...) would not find God's true righteousness.

Therefore, Romans 3:21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
See All... is not dealing with two kinds of salvation but rather with two kinds of righteousness: the righteousness of the law that could not save and the righteousness of Jesus Christ by which we are saved.