A barium study will light up the ____________________ system.

The answer is gastrointestinal because a barium study is a diagnostic imaging procedure specifically designed to visualize the gastrointestinal tract. During this study, a patient ingests a barium sulfate contrast material, which is a radiopaque substance that blocks X-rays. As it moves through the digestive system, the barium outlines the structures of the gastrointestinal tract, including the esophagus, stomach, and intestines, making them visible on X-ray images.

This procedure is particularly useful in identifying abnormalities such as blockages, ulcers, tumors, or other gastrointestinal conditions. While the nervous, cardiovascular, and respiratory systems are crucial components of the body, they do not involve the use of barium studies for diagnostic imaging. Thus, in the context of this question, the gastrointestinal system is the only correct answer.