Which systems of equations have no real number solutions? Check all that apply.y = x2 + 4x + 7 and y = 2 y = x2 – 2 and y = x + 5y = –x2 – 3 and y = 9 + 2xy = –3x – 6 and y = 2x2 – 7x y = x2 and y = 10 – 8x

Set the two expressions for y equal in each system. A gives x² + 4x + 5 = 0, with discriminant 4² − 4(1)(5) = −4, so it has no real solutions. C gives x² + 2x + 12 = 0, with discriminant 2² − 4(1)(12) = −44; D gives 2x² − 4x + 6 = 0, with discriminant (−4)² − 4(2)(6) = −32. A quadratic has no real roots when its discriminant is negative, so the systems are A, C, and D.

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