A solution to the given system of equations is . Which of the following is a possible value of xy

Question

A solution to the given system of equations is . Which of the following is a possible value of xy ?

Accepted Answer

Choice A is correct. Solutions to the given system of equations are ordered pairs that satisfy both equations in the system. Adding the left-hand and right-hand sides of the equations in the system yields , or . Subtracting y from both sides of this equation yields . Taking the square root of both sides of this equation yields and . Therefore, there are two solutions to this system of equations, one with an x -coordinate of 6 and the other with an x -coordinate of . Substituting 6 for x in the second equation yields , or ; therefore, one solution is . Similarly, substituting for x in the second equation yields , or ; therefore, the other solution is . It follows then that if is a solution to the system, then possible values of are and . Only 0 is among the given choices. Choice B is incorrect. This is the x -coordinate of one of the solutions, . Choice C is incorrect and may result from conceptual or computational errors. Choice D is incorrect. This is the square of the x -coordinate of one of the solutions, .

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