Coming late to the discussion. My dad was a Southern Baptist preacher, and I remember as a kid he preached on salvation; that it remains the same through the ages. It always has been "by grace, through faith."
"Abram believed the LORD, and it was credited to him as righteousness." (Genesis 15:6) "For what does the Scripture say? “ Abraham believed God, and it was credited to him as righteousness.” (Romans 4:3)
It is a common misunderstanding that Jews of the Old Testament were saved by works. Contemporary Judaism focuses on works, but it is not the same as 1st cen Judaism. Judaism today thinks more in terms of a national salvation, and the better they keep the commandments in Torah the sooner the messiah will come. 1st cen Judaism thought in terms of both personal and national salvation. Frankly, I think if we looked at it as they did the world might be in less of a mess today.
Works never saved anyone:
"We have all become like one who is unclean, and all our righteous deeds are like a polluted garment. We all fade like a leaf, and our iniquities, like the wind, take us away." (Isaiah 64:6 ESV) No one, then or now can keep the commandments perfectly. So if salvation was by works in the OT, no one would have ever been saved. They, like us were saved by God's grace, His unmerited favor, and their faith in that same God.
The 1st 5 books of Moses, like the rest of our Bible served 2 main purposes: to point us to the Christ (Messiah), and instruct us in how to walk holy beside a Holy God. That's all works are- holiness. As such those works are as much a part of our lives as believers today as they were in the days of Moses, Joshua, Ruth, Daniel, David, ... .
"What good is it, my brothers, if someone says he has faith but does not have works? Can that faith save him? ... So also faith by itself, if it does not have works, is dead." (James 2:14,17 ESV)
Works cannot save us, however because we are saved we should want to do those works:
“If you love me, you will keep my commandments.” (John 14:15 ESV) And nothing in this life stagnates. You like water are either moving forward or you will stagnate, your faith turning rancid. Not to open another debate, but one of the doctrines I cam to question from my youth is "eternal security" as viewed by the Southern Baptists. 2 ways (in my view) you can loose your salvation: 1) rebellion- you can choose to walk away, and 2) stagnation. If we are not living for God ("works") then our faith and our witness are dead, stagnant, useless.
Works cannot save, but they are important to our salvation.