The Old testament is extremely important.
Christ taught and quoted from the Old testament all the time, from God's words. And we live by every Word of God.
It's written that all scripture is given by inspiration from God. Some scriptures to consider :
Luke 4:16-44
16 And He came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read.
17 And there was delivered unto him the book of the prophet Esaias ( Isaiah ). And when he had opened the book, he found the place where it was written,
18 The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised,
19 To preach the acceptable year of the Lord.
20 And he closed the book, and he gave it again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him.
( FYI - The next part that He did not read was "" Isaiah 61: "and the day of vengeance of our God; to comfort all that mourn;" )
John 5:39-47
39 Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me.
46 For had ye believed Moses, ye would have believed me; for he wrote of me.
( Deuteronomy 18:15-19 )
Isaiah 7:14 Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
Matthew 1:23 Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.
2 Timothy 3:16-17
16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
17 That the man of God may be perfect, thoroughly furnished unto all good works.
Proverbs 30:5-6
5 Every word of God is pure: he is a shield unto them that put their trust in him.
Deuteronomy 8:
3 And he humbled thee, and suffered thee to hunger, and fed thee with manna, which thou knewest not, neither did thy fathers know; that he might make thee know that man doth not live by bread only, but by every word that proceedeth out of the mouth of the Lord doth man live.
Matthew 4:4 ( Christ speaking ) But he answered and said, It is written, Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God.
Mark 1:
2 As it is written in the prophets, Behold, I send my messenger before thy face, which shall prepare thy way before thee.
Isaiah 40:
3 The voice of him that crieth in the wilderness, Prepare ye the way of the Lord, make straight in the desert a highway for our God.
4 Every valley shall be exalted, and every mountain and hill shall be made low: and the crooked shall be made straight, and the rough places plain:
5 And the glory of the Lord shall be revealed, and all flesh shall see it together: for the mouth of the Lord hath spoken it.
Luke 11:29 And when the people were gathered thick together, he began to say, This is an evil generation: they seek a sign; and there shall no sign be given it, but the sign of Jonas the prophet. ( Speaking of Jonah )
Matthew 24:15
( Christ quoting the Old testament here also )
15 When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand : )
Acts 8:28-40
28 Was returning, and sitting in his chariot read Esaias the prophet.
29 Then the Spirit said unto Philip, Go near, and join thyself to this chariot.
30 And Philip ran thither to him, and heard him read the prophet Esaias, and said, Understandest thou what thou readest?
31 And he said, How can I, except some man should guide me? And he desired Philip that he would come up and sit with him.
32 The place of the scripture which he read was this, He was led as a sheep to the slaughter; and like a lamb dumb before his shearer, so opened he not his mouth:
33 In his humiliation his judgment was taken away: and who shall declare his generation? for his life is taken from the earth.
34 And the eunuch answered Philip, and said, I pray thee, of whom speaketh the prophet this? of himself, or of some other man?
35 Then Philip opened his mouth, and began at the same scripture, and preached unto him Jesus.