MediumMath· Advanced Math· Nonlinear equations in one variable and systems of equations in two variables· MCQ
A solution to the given system of equations is . Which of the following is a possible value of xy ?
A
0
B
6
C
12
D
36
Correct answer: A
Explanation
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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id cb_question_bank:aaf9b597-1021-4b4e-8e95-682707f02e91 · question 0980fcdd · IBN 035714-DC
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