βDo we then make void the law through faith? God forbid: yea, we establish the lawβ (Rom. 3:31).
In this passage, salvation by βfaithβ is being contrasted to salvation by βworksβ (Rom. 3:27), the works or βdeedsβ of the law (Rom. 3:28). The law demands 100% righteousness to be saved (Gal. 3:10; James 2:10,11). That means to be saved by the deeds of the law, you would have to bend the law to say that God will accept people who are only 75% righteous, or 88% righteous, or even 99% righteous.
But faith in the sacrifice of Christ for our sins doesnβt have to bend the law, itΒ establishesΒ the law. Faith acknowledges that βthe law is holy, andβ¦just, and goodβ (Rom 7:12), but that we are βcarnal, sold under sinβ (Rom 7:14). That is, faith establishes that there is nothing wrong with the law, there is something wrongΒ with us. We canβt keep the law perfectly, so we must place our faith in the Christ who kept it perfectlyΒ for us, and then died a sacrificial death on our behalf.
It was because the righteousness of the law couldnβt be fulfilledΒ by usΒ that Christ βgave HimselfΒ for usβ (Titus 2:14), that βthe righteousness of the law might be fulfilledΒ in usβ by Him (Rom. 8:4). source