SAT Question 1e003284: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. It's given that the graphs of the given equations intersect at the point $\left(x,y\right)$ in the xy-plane. It follows that $\left(x,y\right)$ represents a solution to the system consisting of the given equations. The first equation given is $x=49$. Substituting $49$ for $x$ in the second equation given, $y=\sqrt{x}+9$, yields $y=\sqrt{49}+9$, which is equivalent to $y=7+9$, or $y=16$. It follows that the graphs of the given equations intersect at the point $\left(49,16\right)$. Therefore, the value of $y$ is $16$.