Final answer:
Hypotension is a major contraindication to the administration of both nitroglycerin and morphine.
Step-by-step explanation:
A major contraindication to the administration of both nitroglycerin and morphine is hypotension. Both nitroglycerin and morphine can cause a decrease in blood pressure, and if given to a patient with hypotension, it can further lower their blood pressure to dangerous levels. It is important to assess a patient's blood pressure before administering these medications.