R.L. Dabney: The fall and salvation are through federal representation before God

“Our view of Christ’s substitution under the Covenant of Paradise determines our view of justification. Thus, Adam by nature was righteous, innocent and guiltless; but not yet adopted. The first covenant was given him, that he might by it earn his adoption of life, his elevation from the state of a (holy) servant, to that of a son. He failed in the undertaking, and fell, with his race, into the state of an enemy, both corrupted and guilty. The second Adam steps into the place vacated by the fall of the first, takes up the work where he dropped it; and, while He makes expiation for the guilt, original and actual purchases for all believers a perfect title, not to restoration to that mutable state from which Adam fell, but to that state of adoption, to which he had aspired. My desire is, that the student adopt this view as the touchstone of his doctrine.” (R.L. Dabney, “Systematic Theology”)

Johannes G. Vos: The Covenant of Works parallels the Covenant of Grace

Johannes G. Vos clearly articulates the importance of the covenant of works as parallel to the way of salvation through Christ (the covenant of grace), which makes sense of the federal (covenantal) headship of Adam and Christ, respectively, in Romans 5 (cf. I Cor. 15:21-22, 45-47):

Why is this doctrine of the covenant of works very important to us as Christians? Because it is parallel to the way of salvation through Jesus Christ. Just as the first Adam brought sin and death, so Christ, the second Adam, brings us righteousness and eternal life. Adam was our representative in the covenant of works; Jesus Christ is our representative in the covenant of grace. Those who reject the doctrine of the covenant of works have no right to claim the blessings of the covenant of grace, for the two are parallel, and stand or fall together, as is proved by Romans 5. (Johannes G. Vos, The Westminster Larger Catechism: A Commentary [Phillipsburg, NJ: Presbyterian and Reformed, 2002], 51-52; quoted by Brian Schwertley in his refutation of the Auburn Avenue theology)

Archibald Alexander: Christ satisfied all requirements that the first Adam failed to perform

Archibald Alexander explains, in terms of the covenant of works, that Christ satisfied the penalty and purchased the reward of eternal life for all His elect, given that paying the penalty did not do away with the preceptive requirements of perfect holiness with respect to the law:

Suppose that the first Adam had continued to obey until his probation was finished, would any one think that afterwards either he or his posterity would be freed from the obligation to be holy? Well, what he failed to do, the second Adam has performed, but the obligation to be holy is immutable. It may be asked, does the law of God require a double obedience, one from our surety, and one from ourselves? We answer, that it requires but one righteousness in order to our justification; but it requires that the justified person continue in conformity with its holy precepts. Our obedience is not now required as a condition of justification; to entertain such an opinion would be to leave the covenant of grace, and to go back to the old covenant of works. It would be to fall from grace, as Paul expresses it, that is from the doctrines of grace. Suppose each one of us had a probation for life under the law, and that we had completed our obedience and obtained justification, we should be required to render no more obedience with a view to being justified, for this is supposed to be already done. But the obligation to obey God would not cease, because we were in a justified state. We would still be required to be conformed to the law, because that was our reasonable service, arising out of our natural relations to our Creator, and because holiness is pleasing to God, beneficial to men, and essential to the promotion of our own happiness. (Archibald Alexander, A Treatise on Justification by Faith)