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Choice A is correct. It's given that the graphs of the given equations intersect at the point $\left(x,y\right)$ in the xy-plane. It follows that $\left(x,y\right)$ represents a solution to the system consisting of the given equations. The first equation given is $x=49$. Substituting $49$ for $x$ in the second equation given, $y=\sqrt{x}+9$, yields $y=\sqrt{49}+9$, which is equivalent to $y=7+9$, or $y=16$. It follows that the graphs of the given equations intersect at the point $\left(49,16\right)$. Therefore, the value of $y$ is $16$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.