An inherited degenerative disease of the muscular system where the muscles weaken and atrophy and become replaced with fatty tissue is called

muscular dystrophy

Explanation:

Muscular dystrophies constitute a heterogeneous group of neuromuscular diseases characterized by progressive and irreversible degeneration of the individual's musculature, leading to the development of muscle weakness and loss of motor capacity. These diseases are caused by mutations in various genes that result in the deficiency or loss of function of muscle proteins of significant importance to the proper functioning of the muscle.

Currently, more than 30 forms of muscular dystrophy have been identified. They differ by the mechanism of genetic inheritance, age at onset of manifestation (from birth, childhood, adolescence or adulthood) and severity of symptoms, rate of disease progression and preferentially affected muscles. Muscle dystrophies taken together are common and there is no efficient treatment to prevent disease progression.