SAT Question 4661e2a9: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. The solution to the given system of equations can be found by solving the first equation for $x$, which gives $x=y+1$, and substituting that value of $x$ into the second equation which gives $y+1+y=(y+1{)}^2-3$. Rewriting this equation by adding like terms and expanding $(y+1{)}^2$ gives $2y+1=y^2+2y-2$. Subtracting $2y$ from both sides of this equation gives $1=y^2-2$. Adding $2$ to both sides of this equation gives $3=y^2$. Therefore, it follows that $y=\pm \sqrt{3}$. Substituting $\sqrt{3}$ for $y$ in the first equation yields $x-\sqrt{3}=1$. Adding $\sqrt{3}$ to both sides of this equation yields $x=1+\sqrt{3}$. Therefore, the ordered pair $(1+\sqrt{3},\sqrt{3})$ is a solution to the given system of equations.