SAT Question 2d2ab76b: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. The two equations form a system of equations, and the solutions to the system correspond to the points of intersection of the graphs. The solutions to the system can be found by substitution. Since the second equation gives $y=3$, substituting $3$ for $y$ in the first equation gives $3=x^2-1$. Adding $1$ to both sides of the equation gives $4=x^2$. Solving by taking the square root of both sides of the equation gives $x=\pm 2$. Since $y=3$ for all values of $x$ for the second equation, the solutions are $(2,3)$ and $(-2,3)$. Therefore, the points of intersection of the two graphs are $(2,3)$ and $(-2,3)$.