Some who teach Salvation by faith alone still find it acceptable to teach that in the Old Testament times, people were saved by a mixture of faith and works. This is a tremendously dangerous teaching, which leaves the door open to a works-based Salvation, and nullifies the entire reason for Jesus coming to earth.
This teaching runs into all of the same problems that a New Testament works Salvation runs into. Namely, how many works were required? If you could be good enough to get to Heaven without Jesus, why did He even come to earth?
If works are involved in any manner with your Salvation, there is no more grace, and you must be saved entirely by works. There can be no mixing of the two concepts. You either do it all, or God does it all:
Romans 11:6
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.
If indeed they got to Heaven by works in the Old Testament, they would certainly be able to boast, because the fact is that they are in Heaven as a result of their own diligent efforts. This obviously violates the fact that no one, from any point in history, will be able to boast of themselves about Salvation:
Ephesians 2:8-9
8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
9 Not of works, lest any man should boast.
The reason why our works cannot have anything to do with Salvation is because works can never pay for or cancel out sins. The only way to get to Heaven is to be sinless. And the only thing that has ever been accepted or will ever be accepted as payment for sin is blood atonement (Leviticus 17:11, Hebrews 9:22), and that blood is Jesus Christ's (Hebrews 9:12, Revelation 1:5, Colossians 1:14: 1 John 1:7).
Jesus Christ, "the Lamb slain from the foundation of the world" (Revelation 13:8), is outside of time. Therefore, His atonement, regardless of where it took place chronologically, applies to every last human being to ever exist.
Before Jesus Christ had come, people were saved by placing their trust in the coming Messiah, of whom all the prophets gave witness:
Acts 10:43
43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
I want to make sure you get this, so I'll repeat - all the prophets gave witness to Jesus Christ. Abel? Yes. Abraham? Yes. Jeremiah? Yes. Noah? Yes. David? Yes. All of them preached and believed Salvation by faith alone in the Messiah. All of them. The precise content of that faith varied in accordance with progressive revelation, but every person throughout the ages was saved by grace through faith:
Hebrews 11:13
13 These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth
The Apostle Paul declared that he was preaching the exact same thing as the prophets, who had proclaimed that the Messiah would die and rise again:
Acts 26:22-23
22 Having therefore obtained help of God, I continue unto this day, witnessing both to small and great, saying none other things than those which the prophets and Moses did say should come:
23 That Christ should suffer, and that he should be the first that should rise from the dead, and should shew light unto the people, and to the Gentiles.
This reiterates the fact that every single last one of the prophets preached about the coming Messiah.
We can clearly learn how people were saved before the Law was given by studying Abraham. Three times we are told that Abraham believed God and it was accounted to him for righteousness (James 2:23, Romans 4:3, Galatians 3:6), which is a quotation from Genesis 15:6.
Abraham is given in Romans 4 as an example of someone justified by faith without works:
Romans 4:2-5
2 For if Abraham were justified by works, he hath whereof to glory; but not before God.
3 For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness.
4 Now to him that worketh is the reward not reckoned of grace, but of debt.
5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.
Job, another man who lived before the Law, demonstrated a clear understanding and belief that God would send a redeemer:
Job 19:25-26
25 For I know that my redeemer liveth, and that he shall stand at the latter day upon the earth:
26 And though after my skin worms destroy this body, yet in my flesh shall I see God:
If Abraham was justified by faith apart from works, and Job, the most righteous man in the Bible apart from Jesus Christ, needed a redeemer, it's clear to me that no one got to Heaven before the Law was given without putting their faith in the Messiah.
But what about after the Law was given? Nothing changed. No one has ever been justified in God's sight by the Law:
Romans 3:20
20 Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.
Galatians 3:11
11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith.
The Old Testament system of temple sacrifices did nothing to justify them in an eternal sense before God because they didn't actually take away their sins:
Hebrews 10:4
4 For it is not possible that the blood of bulls and of goats should take away sins.
The phrase "the just shall live by faith", a central motif in the New Testament that is used over and over again to describe the sense in which we are justified (Romans 1:17, Galatians 3:11, Hebrews 10:38), is a quotation from Habakkuk 2:4, and Habakkuk lived under the Law.
David is used in Romans 4 as another witness to the fact that Salvation is by faith without works, and David lived under the Law:
Romans 4:6-8
6 Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,
7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.
8 Blessed is the man to whom the Lord will not impute sin.
Furthermore, if you read the Psalms, David calls God his Savior and talks about trusting in Him many dozens of times (Psalms 25:20, 31:1, 31:5, 32:10, 33:21, 34:8, 34:22, etc. etc.). How can you truly trust in the Lord if your eternal destiny depends on your behavior and obedience to a Law which no one can keep, or has ever kept?
If you bind yourself to keeping the Law for Salvation, you are under a curse (Galatians 3:10), because if you break the smallest point you become as condemned as if you had broken all of it (James 2:10). If you have to keep any point of it to any extent, you have to keep all of it perfectly (Galatians 5:3), which is why you cannot be justified by keeping the Law (Galatians 2:16, 3:11, Romans 3:20).
Peter dealt with this issue because there were people going around then (just like they do now, there's nothing new under the sun) preaching that in addition to faith in Christ you also had to keep the Law to be saved:
Acts 15:5
5 But there rose up certain of the sect of the Pharisees which believed, saying, That it was needful to circumcise them, and to command them to keep the law of Moses.
His rebuke gives us insight into the Salvation of Old Testament saints:
Acts 15:10-11
10 Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear?
11 But we believe that through the grace of the Lord Jesus Christ we shall be saved, even as they.
He says that their fathers who lived under the Law were not able to bear it, therefore implying that they too were saved by grace. And as we've already seen in Romans 11:6, if someone is saved by grace to any extent, works cannot be involved in even the slightest sense, else it has ceased to be grace. Therefore, the Old Testament saints were saved entirely without works, as they were unable to bear the demands of the Law, which required perfection (James 2:10).
Returning to Psalms, note that David defined "saints" as they that hope in the Lord:
Psalm 31:23-24
23 O love the Lord, all ye his saints: for the Lord preserveth the faithful, and plentifully rewardeth the proud doer.
24 Be of good courage, and he shall strengthen your heart, all ye that hope in the Lord.
Saints are "those who are sanctified", and we learn in the New Testament that those who are sanctified are sanctified by faith (Acts 26:18) and perfected forever (Hebrews 10:14).
Psalms has so many examples of exhortations to trust that it would be redundant to list them all. He taught people to trust in the Lord completely, as did his son Solomon (Proverbs 3:5-6, 16:20, 29:25), which would be terrible advice if how well you kept the Law determined your eternal fate.
We are told that if keeping the Law could justify you before God, there would have been no reason for Jesus to come to earth, and His death on the cross was meaningless (Galatians 2:21, 3:21).
If the Israelites kept the Law, they would be blessed physically individually and as a nation (see Deuteronomy chapter 28, for instance). It had nothing to do with them getting to Heaven. The purpose of the Law has always been to point us to the Redeemer, the Messiah (Galatians 3:24).
Note that the New Covenant was not in effect until Jesus Christ died (Hebrews 9:15-18). That means that all four Gospels primarily deal with events involving people living under the Old Testament. That means that passages like this were spoken to people under the Law:
John 6:47
47 Verily, verily, I say unto you, He that believeth on me hath everlasting life.
Jesus taught the exact same thing that all the Old Testament prophets taught, and He preached primarily to people living under that Old Covenant.
And what do we see in His preaching in John, the only book that is written to tell you how to get to Heaven (John 20:31)? Over and over again to the point of redundancy, the message is that any person who believes in Jesus has Everlasting Life (John 3:14-16, 3:18, 3:36, 5:24, 6:35, 6:39-40, 6:47, 11:25-26, 20:31, etc.).
Dispensational Salvationists such as Peter Ruckman assert that John was teaching "Pauline theology", because he wrote his Gospel after Paul wrote the epistles. However, John quotes Jesus Christ - it's not as if he invented what was said or took things out of context to support "Pauline theology". That means that Jesus taught the same things taught in "Pauline theology", and taught them to Jews living under the Old Covenant.
This is a tremendously dangerous heresy because it totally misunderstands the standards that God has. Nothing less than perfect righteousness can appease God, and this teaching is basically that if you try your best, it is (or was, or will be) possible to please Him with less than perfection. This in effect denies that God will be a perfect judge who punishes all iniquity.
In fact, this teaches that people in other times were able or will be able to be saved by filthy rags:
Isaiah 64:6
6 But we are all as an unclean thing, and all our righteousnesses are as filthy rags; and we all do fade as a leaf; and our iniquities, like the wind, have taken us away.
No man has or will ever come to the Father by any other means than the Messiah Jesus Christ (John 14:6). If any man failed to put their trust in God's promised Messiah, at any point in time, they died in their sins (John 8:24).