SAT Question 876a731c: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. Substituting $x^2$ for $y$ in the second equation gives $2x^2+6=2(x+3)$. This equation can be solved as follows: $2x^2+6=2x+6$ (apply the distributive property); $2x^2+6-2x-6=0$ (subtract $2x$ and $6$ from both sides of the equation); $2x^2-2x=0$ (combine like terms); $2x(x-1)=0$ (factor both terms on the left side of the equation by $2x$). Thus, $x=0$ and $x=1$ are the solutions to the system. Since $x>0$, only $x=1$ needs to be considered. The value of $y$ when $x=1$ is $y=x^2=1^2=1$. Therefore, the value of $xy$ is $1\times 1=1$.