Shedd and Hodge: Christ satsified the penalty and precept of the Law for His people

“But the law requires present and perfect obedience, as well as satisfaction for past disobedience. The law is not completely fulfilled by the endurance of penalty only. It must also be obeyed Christ both endured the penalty due to man for disobedience, and perfectly obeyed the law for him; so that He was a vicarious substitute in reference to both the precept and the penalty of the law. By his active obedience He obeyed the law, and by his passive obedience He endured the penalty. In this way his vicarious work is complete.” –William Shedd, "History of Christian Doctrine," quoted by Charles Hodge in “Systematic Theology,” vol. 3

“As Christ obeyed in suffering, his sufferings were as much a part of his obedience as his observance of the precepts of the law. The Scriptures do not expressly make this distinction, as they include everything that Christ did for our redemption under the term righteousness or obedience. The distinction becomes important only when it is denied that his moral obedience is any part of the righteousness for which the believer is justified, or that his whole work in making satisfaction consisted in expiation or bearing the penalty of the law. This is contrary to Scripture, and vitiates the doctrine of justification as presented in the Bible.” –Charles Hodge in “Systematic Theology,” vol. 3

"Christ sustained no other relation to the law, except so far as voluntarily assumed, than that which God himself sustains. But God is not under the law. He is Himself the primal, immutable, and infinitely perfect law to all rational creatures. Christ’s subjection to the law therefore, was as voluntary as his submitting to the death of the cross. As He did not die for Himself, so neither did He obey for Himself. In both forms of his obedience He acted for us, as our representative and substitute, that through his righteousness many might be made righteous." –Charles Hodge in “Systematic Theology,” vol. 3

Charles Hodge: Justification is objective and forensic because it is grounded in extrinsic, imputed righteousness

The nature of justification is determined by its ground. This indeed is an anticipation of another part of the subject, but it is in point here. If the Bible teaches that the ground of justification, the reason why God remits to us the penalty of the law and accepts us as righteous in his sight, is something out of ourselves, something done for us, and not what we do or experience, then it of necessity follows that justification is not subjective. It does not consist in the infusion of righteousness, or in making the person justified personally holy. If the “formal cause” of our justification be our goodness; then we are justified for what we are. The Bible, however, teaches that no man living can be justified for what he is. He is condemned for what he is and for what he does. He is justified for what Christ has done for him. (Charles Hodge, Systematic Theology, vol. III)

Charles Hodge: Refutation of the "Moral Influence" theory of the atonement

The idea that there is no forgiveness with God; that by inexorable law He deals with his creatures according to their subjective state and character, and that therefore the only salvation necessary or possible is sanctification, is appalling. No man is in such an inward state, either during life or at death, that he can stand before God to be dealt with according to that state. His only hope is that God will, and does, deal with his people, not as they are in themselves, but as they are in Christ, and for his sake; that He loves and has fellowship with us although polluted and defiled, as a parent loves and delights in a misshapen and unattractive child. ... Anything that turns the sinner’s regard inward on himself as a ground of hope, instead of bidding him took to Christ, must plunge him into despair, and despair is the portal of eternal death. In any view, therefore, whether as bold rationalistic Deism, or as the most high-toned portraiture of divine love, the moral theory of the atonement presents no rational, because no Scriptural, ground for a sinner’s hope toward God. He must have a better righteousness than his own. He must have some one to appear before God in his stead to make expiation for sin, and to secure for him, independently of his own subjective state, the full pardon of all his offences, and the gift of the Holy Ghost. (Charles Hodge, Systematic Theology, II:3:9:3, Soteriology: Theories of the Atonement: The Moral View)

Christ's atonement and righteousness guarantees salvation to all for whom He served as the Substitute, that God might be just

"The sin of Adam did not make the condemnation of all men merely possible; it was the ground of their actual condemnation. So the righteousness of Christ did not make the salvation of men merely possible, it secured the actual salvation of those for whom He wrought." -Charles Hodge

"If Christ has died for you, you can never be lost. God will not punish twice for one thing. If God punished Christ for your sins He will not punish you. 'Payment God’s justice cannot twice demand; first, at the bleeding Saviour’s hand, and then again at mine.' How can God be just if he punished Christ, the substitute, and then man himself afterwards?" -C.H. Spurgeon

(Both of these quotes are from Lorraine Boettner's Limited Atonement.)

These quotes regarding the atonement answer to the questions that the doctrine of justification seeks to answer: "How can a man be just with God?" and "How can God be just but yet justify the wicked?" Only personal, perfect, and perpetual obedience will suffice; we must be dressed in spotless raiment, untainted in any respect by the defilement of totally depraved flesh. In our case as sinners, in order to be judicially declared "righteous" before God, we must obtain pardon as well as acceptance through perfect, perpetual law-keeping, as well as an infinite sacrifice for our sins -- both of which are impossible for us to perform. Because Christ served as our substitute in His passive obedience -- taking the guilt, curse, and penalty for sin upon Himself through imputation -- God has justly punished sin once and for all for His elect. Christ has also purchased the eternal reward of glorified life for His elect by His active obedience, His lifetime of perfect and perpetual Law-keeping from start to finish -- fulfilling all righteousness -- that is imputed to us. The question now becomes: "How can God be just if He punishes a man, for whom Christ died, with an eternity of hell apart from glorified life with God?"

Christ died that God might be just and the justifier of those who believe in Jesus (Rom. 3:26). Those who, by the instrumentality of faith alone, receive and rest in the person and work of Christ alone -- His active and passive obedience -- are pardoned and accepted, declared righteous before God's throne, and will obtain the eternal reward of glorified life that Christ purchased. God would be unjust to twice punish sin, first in the person of Christ through imputation of man's guilt when Christ bore their sins upon the tree, and secondly in the punishment of the man himself for the same sin. Arminianism and all other deviant forms of soteriology make God out to be an unjust judge. Either God is supposed to pardon and accept men on grounds other than an infinite sacrifice to pay the penalty for sins, as well as perfect, perpetual, and personal Law-keeping in every word, thought, deed, and motive; or He is supposed to exact the penalty for sin both from Christ and from some of those for whom He was supposed to die.

Charles Hodge: God, who is perfectly just, requires perfect righteousness in those whom He accepts

"The Apostle, having taught that God is just, i.e., that He demands the satisfaction of justice, and that men are sinners and can render no such satisfaction themselves, announces that such a righteousness has been provided, and is revealed in the Gospel. It is not our own righteousness, which is of the law, but the righteousness of Christ, and, therefore, the righteousness of God, in virtue of which, and on the ground of which, God can be just and yet justify the sinner who believes in Christ. As long as the Bible stands this must stand as a simple statement of what Paul teaches as to the method of salvation. Men may dispute as to what he means, but this is surely what he says." –Charles Hodge in “Systematic Theology,” vol. 3

Charles Hodge: Christ's righteousness, not works or faith, is the ground of justification

Charles Hodge explains the ground of justification as the righteousness of Christ -- His penal (passive/negative) and preceptive (active/positive) obedience -- which refutes all notions of inherent righteousness within works or even within the true faith by which we take hold of and become united with Christ:

“The ground of justification is the righteousness of Christ, active and passive, i.e., including his perfect obedience to the law as a covenant, and his enduring the penalty of the law in our stead and on our behalf.” –Charles Hodge, Systematic Theology (vol. 3)

Charles Hodge: We are justified by faith that unites us to Christ as our righteousness

Charles Hodge explains that faith is not inherently virtuous so as to provide a meritorious grounds for acceptance with God, but that justifying righteousness is alien to ourselves:

It is not on account of any virtue or goodness in faith, but as it unites us to Christ, and involves the acceptance of Him as our righteousness. Thus it is we are justified “by faith alone, without any manner of virtue or goodness of our own.” (Charles Hodge, Systematic Theology, vol. 3: Justification)