SAT Question 84e5e36c: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. Since the point $\left(x,y\right)$ is an intersection point of the graphs of the given equations in the xy-plane, the pair $\left(x,y\right)$ 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.