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Romans 10:4 For Christ is the end of the law for righteousness to everyone who believes.
 
Nothing could be clearer. The Law was never given to make humans righteous. It never had that power, for we, totally depraved, could never keep it. Rather, the Law, showing our sin, leads us to Christ.
 
It has always led God's people to God's mercy through substitutionary sacrifice. In the Old Testament the imperfect sacrifice of animals, that could never really take away sin, pointed to the one who could, Christ. In the New Testament, it becomes even clearer how God, in his mercy, will offer us righteousness: by faith in Christ, not by perfection in keeping the Law.
 
Calvin. "He shows that he is a false interpreter of the law, who seeks to be justified by his own works; because the law had been given for this end, ― to lead us as by the hand to another righteousness: nay, whatever the law teaches, whatever it commands, whatever it promises, has always a reference to Christ as its main object; and hence all its parts ought to be applied to him. But this cannot be done, except we, being stripped of all righteousness, and confounded with the knowledge of our sin, seek gratuitous righteousness from him alone."
 
Of course, the Law also is given to restrain evil in the world and to guide those who have found their righteousness in Christ in how to live uprightly in this world. But with the Old Testament sacrificial system partly, and with Christ perfectly, we see that the Law was never given as a way for people to become righteous before God. Given after the fall into sin, we could never benefit from it that way.
 
Christ is not the end of the law. He is the end of the law for obtaining righteousness. Rather, we find our righteousness by faith in Christ!
Lord, let me believe in him and rest in the righteousness that he gives, not in any righteousness I think I may have earned!