Final answer:
Macrophages are the immune system cells primarily responsible for the destruction of old cells and invasive micro-organisms.
Step-by-step explanation:
The type of immune system cell that is primarily responsible for the destruction of old cells and invasive micro-organisms is Macrophages. Macrophages are phagocytes, which means they have the ability to engulf and digest pathogens. They play a crucial role in the innate immune response by destroying these pathogens and clearing them from the body.