x 2 + y + 10 = 10 8 x + 16 - y = 0 The solution to the

Question

x 2 + y + 10 = 10 8 x + 16 - y = 0 The solution to the given system of equations is x , y . What is the value of x ?

Accepted Answer

Choice B is correct. Adding y to each side of the second equation in the given system of equations yields 8 x + 16 = y . Substituting 8 x + 16 for y in the first equation yields x 2 + 8 x + 16 + 10 = 10 . Subtracting 10 from each side of this equation yields x 2 + 8 x + 16 = 0 . This equation can be rewritten as x + 4 2 = 0 . Taking the square root of each side of this equation yields x + 4 = 0 . Subtracting 4 from each side of this equation yields x = - 4 . Therefore, the value of x is - 4 . Choice A is incorrect. This is the value of y , not x . Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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