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Choice A is correct. The given point, $\left(8,2\right)$, 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, $\left(8,2\right)$ 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 $\left(8,2\right)$ make the inequalities $x>0$ and $y>0$ true, the point $\left(8,2\right)$ 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.