Nonlinear equations in one variable and systems of equations in two variables SAT question

Choice B is correct. Since the point $(x,y)$ is an intersection point of the graphs of the given equations in the xy-plane, the pair $(x,y)$ should satisfy both equations, and thus is a solution of the given system. According to the first equation, $y=76$. Substituting $76$ in place of $y$ in the second equation yields $x^2-5=76$. Adding $5$ to both sides of this equation yields $x^2=81$. Taking the square root of both sides of this equation yields two solutions: $x=9$ and $x=-9$. Of these two solutions, only $-9$ is given as a choice.

Choice A 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. This is the value of coordinate $y$, rather than $x$, of the intersection point $(x,y)$.