An accounting system that recognizes income only when it is actually received operates on which basis?

The accounting system that recognizes income only when it is actually received operates on the cash basis. This method focuses on the actual cash transactions—revenues are recorded only when cash is received, and expenses are recorded when cash is paid out. Such an approach provides a straightforward view of cash flow and is particularly useful for small businesses or sole proprietors who might not have the complex accounting needs of larger entities.

In contrast, the accrual basis recognizes income when it is earned and expenses when they are incurred, regardless of when the cash changes hands. A hybrid basis combines aspects of both accrual and cash methods, allowing for flexibility in recognizing income and expenses. The modified cash basis allows for certain accrual principles while primarily using the cash method, but it does not strictly adhere to the single cash basis principle that the question specifies. Therefore, the cash basis is distinctively characterized by its focus on the timing of cash receipt, making it the correct answer.