The sacrificial system of the Old Testament was only temporary until Jesus gave us a permanent solution. The old system acted just like a credit card company. The company covers the price of a purchase until we pay the bill.
The Sacrificial System was Only Temporary
Paul explained why the New Covenant of Jesus could replace the Old Covenant. Galatians 3: 23 Before the way of faith in Christ was available to us, we were placed under guard by the law. We were kept in protective custody, so to speak, until the way of faith was revealed.
24 Let me put it another way. The law was our guardian until Christ came; it protected us until we could be made right with God through faith. 25 And now that the way of faith has come, we no longer need the law as our guardian.
Paul uses the image of a guardian for an underage child for the old sacrificial system. A guardian becomes outdated when the child becomes an adult. So too, did the sacrificial system when Jesus paid the price for our sin.
A Modern Illustration of a Credit Card
The relationship of the sacrificial system to the New Covenant of Jesus can be illustrated by a credit card. A credit card is simply a piece of plastic, but it is accepted as cash. The credit card company covers the price of purchase until the owner of the card pays the bill at the beginning of the month.
In this sense, the sacrifices under the Old Covenant covered the sins of the people and foreshadowed the day when Jesus would make full payment on the cross. Because Jesus has paid not only all past sins, but all future ones as well, there is no need for the sacrificial system today.
Hebrews 9: 12 With his (Jesus’) own blood—not the blood of goats and calves—he entered the Most Holy Place once for all time and secured our redemption forever.
13 Under the old system, the blood of goats and bulls and the ashes of a heifer could cleanse people’s bodies from ceremonial impurity. 14 Just think how much more the blood of Christ will purify our consciences from sinful deeds so that we can worship the living God. For by the power of the eternal Spirit, Christ offered himself to God as a perfect sacrifice for our sins. 15 That is why he is the one who mediates a new covenant between God and people, so that all who are called can receive the eternal inheritance God has promised them. For Christ died to set them free from the penalty of the sins they had committed under that first covenant.
To hear how the New Covenant of Jesus is just like a credit card, listen here:
 Kevin Howard & Marvin Rosenthal, The Feasts of the Lord, Thomas Nelson Publishing, Nasheville, TN, 1997, p 131.