Plants and animals coexist in balanced ecosystems through a complex network of interactions that support each other's survival. Plants provide oxygen, food, and shelter for animals, while animals help in seed dispersal, pollination, and nutrient recycling for plants. This interdependence helps to maintain the delicate balance of energy flow and nutrient cycling within the ecosystem, ensuring the well-being of all organisms within it. Additionally, competition, predation, and symbiotic relationships also play crucial roles in regulating populations and maintaining equilibrium in the ecosystem.