Plants and animals coexist in balanced ecosystems through various interconnected relationships. Plants provide oxygen, food, and shelter for animals, while animals help in pollination, seed dispersal, and nutrient cycling for plants. This mutual dependency ensures that both plant and animal populations remain in check, preventing overpopulation or extinction of any species. Additionally, the presence of predators helps control prey populations, maintaining balance in the ecosystem. Overall, the interactions and relationships between plants and animals contribute to the stability and sustainability of a balanced ecosystem.