Non-potable water may be used for flushing a water closet if it is piped in an _______ system.

Using non-potable water for flushing a water closet is permissible when it is piped in an independent system. An independent system means that the plumbing for non-potable water is separate and distinct from the potable water system. This is crucial for preventing any potential contamination of the potable water supply, which must remain clean and safe for drinking and other domestic uses. By having a standalone system, regulations and safety protocols can effectively ensure that non-potable water does not mix with the water intended for consumption.

The other terms do not accurately describe the separation needed to maintain safety and health standards. An integrated or interconnected system would imply a connection between potable and non-potable water supplies, which could lead to cross-contamination. An open system typically refers to a system exposed to environmental factors and does not inherently denote the necessary separation of water supplies. Therefore, an independent system is the correct designation for safely using non-potable water for flushing purposes.