Law is a system of demand: do this and live. Grace is a gift of supply: Christ lived and died, now receive it. Law tells you what to do but gives no power to do it. Grace gives you Christ Himself. You are no longer under the one; you live under the other.
The Grace Answer
Law and grace are not two flavors of the same thing. They are two opposite principles for being made right with God, and confusing them is behind most of the anxiety Christians carry.
Law is the system of demand. It says: do this and you will live. It sets a perfect standard, and it is holy and good at what it does, which is to expose sin and show you that you cannot meet the standard on your own. What law never does is give you the power to obey. It can command, but it cannot enable. The law was given through Moses, but grace and truth came through Jesus Christ.
Grace runs the other direction
Grace is the system of supply. Where law demands, grace provides. It says: Christ has already lived the life and paid the debt, now receive it as a gift. Law points to what you owe. Grace points to what He gave. And grace does what law never could, it changes you from the inside, because it gives you not just a standard but a Savior who lives in you.
This is why Paul says something that sounds shocking until you sit with it: you are not under law but under grace. For the believer, the law is no longer the basis of your relationship with God. Christ is the end of the law for righteousness to everyone who believes. Not the end of morality, but the end of law-keeping as the way you are made right.
Jesus said no one puts new wine into old wineskins, and this is why. Law and grace run on opposite principles, demand and gift, and forcing them together bursts the whole thing. You cannot be a little bit under law any more than you can be a little bit alive. None of this means God was harsh before and kind afterward. Grace was always His heart, seen in Eden, in the promise to Abraham, in every rescue of a people who could not keep their end. What changed at the cross was not God's character but the covenant, the basis on which you are made right. Mixing the two ruins both. Add law to grace and you no longer have grace, because grace by definition is unearned. Try to live the Christian life by demand rather than supply and you get exhausted and defeated. But receive everything as gift, and you find that the life the law could only command starts flowing out of you naturally, produced by grace rather than pressured by rules.