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Choice A is correct. The solution to a system of equations is the ordered pair $\left(x,y\right)$ that satisfies all equations in the system. It's given by the first equation in the system that $x+7=10$. Substituting $10$ for $x+7$ into the second equation yields ${10}^2=y$, or $y=100$. The x-coordinate of the solution to the system of equations can be found by subtracting $7$ from both sides of the equation $x+7=10$, which yields $x=3$. Therefore, the ordered pair $\left(3,100\right)$ is a solution to the given system of equations.

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.