How the law of Moses points to Christ

The apostle Paul says that the law was a tutor to bring believers in Galatia to Christ:

Galatians 3 v 24

24 So that the law has become our tutor to bring us to Christ, that we might be justified by faith. 
The law of Moses tells us several things to help us to understand what Christ achieved:

The letter to the Hebrews shows that the law of Moses couldn't permantly take away sin. That was only possible by faith in Jesus' sacrifice:

Hebrews 10 v 1 to 4

For the law, having a shadow of the good to come, not the very image of the things, can never with the same sacrifices year by year, which they offer continually, make perfect those who draw near.  2  Or else wouldn’t they have ceased to be offered, because the worshippers, having been once cleansed, would have had no more consciousness of sins? But in those sacrifices there is a yearly reminder of sins. For it is impossible that the blood of bulls and goats should take away sins. that the law has become our tutor to bring us to Christ, that we might be justified by faith. 
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