SAT Question 58443765: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. The second equation in the given system is $y=5x^2+4$. Substituting $5x^2+4$ for $y$ in the first equation of the given system yields $5x^2+4=5x+4$. Subtracting $4$ from both sides of this equation yields $5x^2=5x$. Subtracting $5x$ from both sides of this equation yields $5x^2-5x=0$. Factoring out a common factor of $5x$ from the left-hand side of this equation yields $5x(x-1)=0$. It follows that $5x=0$ or $x-1=0$. Dividing both sides of the equation $5x=0$ by $5$ yields $x=0$. Substituting $0$ for $x$ in the equation $y=5x+4$ yields $y=5(0)+4$, or $y=4$. Therefore, a solution to the given system of equations is the ordered pair $(0,4)$.