Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.

Set the two expressions for y equal: −x² + 6x + 16 = −4x + 37. Rearranging gives x² − 10x + 21 = 0, which factors as (x − 3)(x − 7) = 0, so x = 3 or x = 7. Substituting into y = −4x + 37 gives y = 25 when x = 3 and y = 9 when x = 7. The solutions are (3, 25) and (7, 9), choice C.

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