'The Law and the Prophets'
Only blood from the sacrifice can seal the covenant of God. Since God is Spirit and without flesh and blood, He will seal His covenant with the blood of any acceptable animal sacrifice.
First Covenant with Adam
Gen 2:16-17 And the Lord God commanded the man, saying, "Of every tree of the garden you may freely eat; but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die."
God made a covenant with Adam that if he ate from the tree of knowledge he would die. After Adam and Eve broke the covenant God killed an animal so that the covenant was sealed and in force. Immediately, God drove them out from the garden of Eden for without the tree of life they would surely die.
Gen 3:21, 24 Also for Adam and his wife the Lord God made tunics of skin, and clothed them... So He drove out the man; and He placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life.
Covenant with Abraham
Gen 15:4-5, 9 And behold, the word of the Lord came to him, saying, "This one shall not be your heir, but one who will come from your own body shall be your heir." Then He brought him outside and said, "Look now toward heaven, and count the stars if you are able to number them." And He said to him, "So shall your descendants be"... So He said to him, "Bring Me a three-year-old heifer, a three-year-old female goat, a three-year-old ram, a turtledove, and a young pigeon."
After God had made the covenant with Abraham that his seeds would be as numerous as the stars in the sky, He demanded Abraham for the blood of animals to seal the covenant. Abraham fulfilled the blood of the covenant by killing the required animals.
Gen 15:10 Then he brought all these to Him and cut them in two, down the middle, and placed each piece opposite the other; but he did not cut the birds in two.
Covenant with Israelites
Heb 9:18-20 Therefore not even the first covenant was dedicated without blood. For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and goats, with water, scarlet wool, and hyssop, and sprinkled both the book itself and all the people, saying, "This is the blood of the covenant which God has commanded you."
With the Israelites, Moses used the blood of both calves and goats as blood of the covenant.
The New Covenant
Mat 26:27-28 Then He took the cup, and gave thanks, and gave it to them, saying, "Drink from it, all of you. For this is My blood of the new covenant, which is shed for many for the remission of sins."
Our Lord Jesus was a devout Jew and He kept the Law. Towards the end of His ministry, He was telling them that He was their Messiah, the light of the world, the way, the truth and the life, etc. yet all His words, teachings, commandments, etc. were not in force for it had not been sealed by the blood of the covenant (His death) and the Old Covenant was still in force then.
The Old Covenant was made obsolete at His death. The death of the Testator (Jesus) on the cross became the blood of the covenant thereby establishing the New Covenant and putting all His commandments, words, teachings, etc. into force for all His believers.
Heb 9:16-17 For where there is a testament, there must also of necessity be the death of the testator. For a testament is in force after men are dead, since it has no power at all while the testator lives.