Galatians 3:21

Having thus sharply contrasted the two covenants, the Apostle anticipates an objection -You say that God is One. He is the Author both of the law and of the promises. How then can there be the opposition between them which your argument would imply?" To this the answer is decisive. The difference is such as to display a marked contrast, not such as to involve antagonism. Otherwise God might seem in giving the law to have retracted the promises. Away with such a supposition.

for if there had been a law given … by the law Life had been forfeited by sin; life must be recovered by righteousness. The promiseassured life to the believer through righteousness imputed; the lawoffered life as the reward of a perfect obedience. Had the conditions of the law been less strict, or had man been able to fulfil them, then righteousness (and life) had come to men from the law. Hence there is no antagonism between the two covenants. -To give life" was the end of both. The law failed to do this; the promise succeeded. Man could not obey perfectly: he could believe, and so obtain life.