The point ( 8 , 2 ) in the xy -plane is a solution to which of the following systems

Question

The point ( 8 , 2 ) in the xy -plane is a solution to which of the following systems of inequalities?

Accepted Answer

Choice A is correct. The given point, 8 , 2 , is loed in the first quadrant in the xy -plane. The system of inequalities in choice A represents all the points in the first quadrant in the xy -plane. Therefore, 8 , 2 is a solution to the system of inequalities in choice A. Alternate approach: Substituting 8 for x in the first inequality in choice A, x > 0 , yields 8 > 0 , which is true. Substituting 2 for y in the second inequality in choice A, y > 0 , yields 2 > 0 , which is true. Since the coordinates of the point 8 , 2 make the inequalities x > 0 and y > 0 true, the point 8 , 2 is a solution to the system of inequalities consisting of x > 0 and y > 0 . Choice B is incorrect. This system of inequalities represents all the points in the fourth quadrant, not the first quadrant, in the xy -plane. Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the xy -plane. Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the xy -plane.

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