x 2 + y + 10 = 10 8 x + 16 - y = 0

Choice B is correct. Adding $y$ to each side of the second equation in the given system of equations yields $8x+16=y$. Substituting $8x+16$ for $y$ in the first equation yields $x^2+8x+16+10=10$. Subtracting $10$ from each side of this equation yields $x^2+8x+16=0$. This equation can be rewritten as ${\left(x+4\right)}^2=0$. Taking the square root of each side of this equation yields $x+4=0$. Subtracting $4$ from each side of this equation yields $x=-4$. Therefore, the value of $x$ is $-4$.

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

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

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