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Good requirements and design reduce future maintenance because the system is more likely to meet business and user needs correctly from the beginning.

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The earlier an error is discovered, the cheaper it is to correct. Good analysis reduces late changes, which lowers overall development cost.

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Many software errors are introduced during the requirements and design phases, but they may not be discovered until much later, when they are far more expensive to fix. Therefore, careful systems analysis and design are important for identifying and preventing errors early.
Summary
Systems analysis and design are important because decisions made early affect the entire software lifecycle. Maintenance accounts for a large portion of total system cost, and the cost of fixing errors increases as a project moves from requirements to design, coding, testing, and operation. Many software errors originate during requirements but are not discovered until later. Therefore, carefully discovering and validating requirements and designing the system correctly early can reduce errors, late changes, maintenance work, and overall cost