Which represents the solution(s) of the system of equations, y = x2 – 4x – 21 and y = –5x – 22? Determine the solution set algebraically.

Set the two expressions for y equal: x² − 4x − 21 = −5x − 22. Rearranging gives x² + x + 1 = 0, whose discriminant is 1 − 4(1)(1) = −3. Since the discriminant is negative, there are no real solutions, so the solution set is no solutions.

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