The answer is sixfold:

(1) The law was added because of transgressions, i.e. to give to sin the character of transgression.

(a) Men had been sinning before Moses, but in the absence of law their sins were not put to their account. Romans 5:13. The law gave to sin the character of “transgression,” i.e. of personal guilt.

(b) Also, since men not only continued to transgress after the law was given, but were provoked to transgress by the very law that forbade it Romans 7:8, the law conclusively proved the inveterate sinfulness of man's nature Romans 7:11-13.

(2) The law, therefore, “concluded all under sin” Romans 3:19,20,23.

(3) The law was an ad interim dealing, “till the seed should come”. Galatians 3:19.

(4) The law shut sinful man up to faith as the only avenue of escape. Galatians 3:23.

(5) The law was to the Jews what the pedagogue was in a Greek household, a ruler of children in their minority, and it had this character “unto” i.e. until Christ Galatians 3:24.

(6) Christ having come, the believer is no longer under the pedagogue. Galatians 3:25
because of for the sake, i.e. in order that sin might be made manifest as transgression. See, Romans 4:15; 5:20; 7:7,13.

Galatians 3:19

Wherefore then serveth the aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law? It was added because of aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law.

Romans 5:13

(For until the law sin was in the world: but sin is not aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law when there is no law.

Romans 7:8

But sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law sin was dead.

Romans 7:11-13

11 For sin, taking occasion by the commandment, aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law me, and by it slew me.

12 Wherefore the law is aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law, and the commandment holy, and just, and good.

13 Was then that which is good made death unto me? God forbid. But sin, that it might appear sin, working death in me by that which is good; that sin by the commandment might become aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law.

Romans 3:19-20, 23

19 Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law, and all the world may become aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law before God.

20 Therefore by the deeds of the law there shall no flesh be aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law in his sight: for by the law is the aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law of sin.

23 For all have sinned, and come short of the aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law of God;

Galatians 3:23-25

23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law.

24 Wherefore the law was our aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law to bring us unto Christ, that we might be justified by faith.

25 But after that faith is aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law, we are no longer under a schoolmaster.

Romans 4:15

Because the law worketh wrath: for where no law is, there is no aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law.

Romans 5:20

Moreover the law entered, that the offence might abound. But where sin aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law, grace did much more abound:

Romans 7:7

7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, aboundedcomedeceivedexceeding sinfulgloryguiltyholyimputedjustifiedknowledgelawmediatorrevealedschoolmasterstoppedThou shalt not covettransgressiontransgressionswithout the law.