SAT Question 1697ffcf: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

The intersection points of the graphs of $y=3x^2-14x$ and $y=x$ can be found by solving the system consisting of these two equations. To solve the system, substitute $x$ for $y$ in the first equation. This gives $x=3x^2-14x$. Subtracting $x$ from both sides of the equation gives $0=3x^2-15x$. Factoring $3x$ out of each term on the left-hand side of the equation gives $0=3x(x-5)$. Therefore, the possible values for $x$ are $0$ and $5$. Since $y=x$, the two intersection points are $(0,0)$ and $(5,5)$. Therefore, $a=5$.