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Algebra / Linear inequalities in one or two variables Difficulty: Easy

The point $left parenthesis 8 comma 2 right parenthesis$ in the xy-plane is a solution to which of the following systems of inequalities?

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Explanation

Choice A is correct. The given point, $left parenthesis 8 comma 2 right parenthesis$ , is located 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, $left parenthesis 8 comma 2 right parenthesis$ is a solution to the system of inequalities in choice A.

Alternate approach: Substituting $8$ for $x$ in the first inequality in choice A, $x greater than 0$ , yields $8 greater than 0$ , which is true. Substituting $2$ for $y$ in the second inequality in choice A, $y greater than 0$ , yields $2 greater than 0$ , which is true. Since the coordinates of the point $left parenthesis 8 comma 2 right parenthesis$ make the inequalities $x greater than 0$ and $y greater than 0$ true, the point $left parenthesis 8 comma 2 right parenthesis$ is a solution to the system of inequalities consisting of $x greater than 0$ and $y greater than 0$ .

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.