Neither testament would be complete without the other. One is the plant in full bloom, the other the seedbed. The roots of Christianity are buried deep in Judaism. The Old is fulfilled in the New, the New is built on the Old. For instance, Leviticus "lives" when studied in the light of Hebrews, and Hebrews is impossible to completely understand without Leviticus.
Our writer believed God wrote the Old Testament. Hebrews gives abundant proofs of the verbal inspiration of Scripture. In referring to Old Testament passages, our writer usually makes no mention of an author's name, but instead speaks of the passages as emanating from God Himself.