Grace Alone through Faith Alone in Christ Alone: God's Justification and Sanctification Intersection

“And you shall put the mercy seat on the top of the ark, and in the ark you shall put the testimony that I shall give you. There I will meet with you, and from above the mercy seat, from between the two cherubim that are on the ark of the testimony, I will speak with you about all that I will give you in commandment for the people of Israel.” Exodus 25:21-22

The Mercy Seat sits above the Ark of the Covenant of the Old Testament in which is contained the Ten Commandments of the Law. This is a type pointing to Jesus who on the cross bore the penalty of our sins and fulfilled the righteous demand of that Law. It is there that God meets with his people.

Our imperfect obedience (i.e. believers' obedience in of itself is still measured as sinful before God's holy and unyielding standard) does not attain to the righteouseness of the Law. Nonetheless it is accepted by God our Father for Christ's sake alone, the Mercy Seat who covers our sins and our less-than-righteous good works. Regarding those imperfect works of believers the Westminster Confession of Faith states -

Notwithstanding, the persons of believers being accepted through Christ, their good works also are accepted in him; not as though they were in this life wholly unblamable and unreprovable in God's sight; but that he, looking upon them in his Son, is pleased to accept and reward that which is sincere, although accompanied with many weaknesses and imperfections. WCF 16:6 

Through faith alone we are united with Christ. Now being identified with him through faith, not only our flawed persons are accepted and rewarded but also our flawed works. 

Grace alone through faith alone in Christ alone - God's justification and sanctification formula!

Calvin: Acceptable Good Works Justified By Faith Alone

"I say that it is owing to free imputation that we are considered righteous before God; I say that from this also another benefit proceeds, viz., that our works have the name of righteousness, though they are far from having the reality of righteousness.  

"In short, I affirm, that not by our own merit but by faith alone, are both our persons and works justified; and that the justification of works depends on the justification of the person, as the effect on the cause. Therefore, it is necessary that the righteousness of faith alone so precede in order, and be so pre-eminent in degree, that nothing can go before it or obscure it."

John Calvin, Acts of the Council of Trent with the Antidote

Purpose of the Law - To Humble Us & Point Us to the Gospel

Now it is evident that no one is justified before God by the law, for "The righteous shall live by faith."
But the law is not of faith, rather "The one who does them shall live by them." 
- Galatians 3:11-12

“Notice that Paul explains his meaning at some length here for us to comprehend why he separates the righteousness of the law and the righteousness of faith, showing us that they are incompatible and can no more be mixed together than fire and water. Not that there is any contradiction between the law and the gospel (as I have already made clear), for we know that they both proceed from the same God. But we must remember God’s purposes, as we have said all along. By giving us the righteousness of the law, he intended to humble us. Next, we will come before him realising we are condemned; this we would never have done if he had not revealed to us our own poverty. When we read that God promises justification if we serve him aright, he is saying in effect, ‘Poor creatures, what worth or value do you have in and of yourselves? Weigh up my commandments and consider what they involve, and then reflect upon how each of you have lived. This will make you feel as if you could drown in self-despair.’ Yet, though God speaks in this vein, he also grants a remedy —‘Come’, he says, ‘to the teachings of the gospel’. And what are they? Paul quotes the expression of Habakkuk, from chapter two and the fourth verse: ‘The just shall live by his faith’...

“[Paul] always taught that faith leads us to find salvation in God alone. The law, though it may appear to be teaching something very different, actually shows us that there is no life in us at all, if we understand it aright. The law says, ‘Work hard and do what you can to obtain paradise.’ Why does it say this? Not to feed man’s vain confidence in his own merits —certainly not! Rather, to prepare us to receive the grace of the Lord Jesus Christ in humility.”

John Calvin. Sermon on Galatians 3:11-12

The Five Solas of the Reformation...

Scripture Alone
VI. Of the Sufficiency of the Holy Scriptures for Salvation.
 Holy Scripture containeth all things
necessary to salvation: so that whatsoever is not read therein, nor may be proved thereby, is not to be required of any man, that it should be believed as an article of the Faith, or be thought requisite or necessary to salvation. In the name of the Holy Scripture we do understand those canonical Books of the Old and New Testament, of whose authority was never any doubt in the Church.
Articles of Religion, The Church of England

Grace Alone
Moreover, the message of free reconciliation with God is not promulgated for one or two days, but is declared to be perpetual in the Church, (2 Corinthians 5:18, 19.) Hence believers have not even to the end of life any other righteousness than that which is there described. Christ ever remains a Mediator to reconcile the Father to us, and there is a perpetual efficacy in his death, viz., cleansing, satisfaction, expiation; in short, perfect obedience, by which all our iniquities are covered. In the Epistle to the Ephesians, Paul says not that the beginning of salvation is of grace, but "by grace are ye saved," "not of works, lest any man should boast," (Ephesians 2:8, 9.)

John Calvin. Institutes of Religion. 3.14.11

Faith Alone
"For the Reformation, reconciliation precedes sanctification... Calvin insists that reconciliation means that the Christian is connected to the perfect righteousness of Christ by that faith that looks away from itself, which is [the] only… instrument of receiving the work of Christ." Faith is the vessel in which the riches of Christ's work are brought to us - reconciling us to God... Faith alone, which looks to Christ alone, has its works, but its works, its fruits, or its outcome are in no way part of justification.” … To say that one is saved by "grace alone" is not enough. The medieval [Roman Catholic] theologians taught that - that grace alone worked to so transform and sanctify one as to be the basis for final justification. Yet such improved life is still imperfect. What one needs to stand in the judgment is a perfect righteousness!

… ”Paul indeed taught that faith stands alone in receiving justification from the work of Christ (Rom. 3:24-26). Justification is not received or maintained by any kind of working, any kind of moral improvement, or any kind of sanctifying moral improvement."

… Peace with God comes only through faith in Christ alone - His merit, His sacrifice and satisfaction for sin...

As Luther wrote, "A man is justified, not by the works of the law, by by faith alone.”
Dr. Robert Godfrey

Christ Alone
If Christ provides only a part of our salvation, leaving us to provide the rest, then we are still hopeless under the load of sin. For no matter how small the gap which must be bridged before salvation can be attained, the awakened conscience sees clearly that our wretched attempt at goodness is insufficient even to bridge that gap. The guilty soul enters again into the hopeless reckoning with God, to determine whether we have really done our part. And thus we groan again under the old bondage of the law. Such an attempt to piece out the work of Christ by our own merit, Paul saw clearly, is the very essence of unbelief; Christ will do everything or nothing, and the only hope is to throw ourselves unreservedly on His mercy and trust Him for all.

J. Gresham Machen: Christianity and Liberalism

To God Be The Glory Alone
And because all this is brought to pass through the only merits and deservings of our Saviour Christ and not through our merits or through the merit of any virtue that we have within us or of any work that cometh from us, therefore in that respect of merit and deserving we forsake, as it were, altogether again faith, works, and all other virtues. For our own imperfection is so great through the corruption of original sin, that all is imperfect that is within us: faith, charity, hope, dread, thoughts, words, and works, and therefore is not apt to merit and deserve any part of our justification for us. And this form of speaking use we in the humbling of ourselves to God and to give all the glory to our Saviour Christ, who is best worthy to have it…

And the said benefits of God, deeply considered, move us for his sake also to be ever ready to give ourselves to our neighbours and, as much as lieth in us, to study with all our endeavour to do good to every man. These be the fruits of true faith: to do good as much as lieth in us to every man, and above all things and in all things to advance the glory of God, of whom only we have our sanctification, justification, salvation and redemption; to whom be ever glory, praise, and honour, world without end. Amen.
Thomas Cranmer, Sermon on the Salvation of Man