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Choice D is correct. Since the graphs of the equations in the given system intersect at the point $\left(x,y\right)$, the point $\left(x,y\right)$ represents a solution to the given system of equations. The first equation of the given system of equations states that $x=8$. Substituting $8$ for $x$ in the second equation of the given system of equations yields $y=8^2+8$, or $y=72$. Therefore, the value of $y$ is $72$.

Choice A is incorrect. This is the value of $x$, not $y$.

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

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