SAT Question 19fdf387: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. Since the graph of $y=x+3$ intersects the graph of $y=2x-6$ at the point $(a,b)$, the ordered pair $(a,b)$ is the solution to the system of linear equations consisting of $y=x+3$ and $y=2x-6$, and the value of $a$ is the value of $x$ in the solution of this system. Since both $x+3$ and $2x-6$ are equal to $y$, it follows that $x+3=2x-6$. Subtracting $x$ from and adding $6$ to both sides of the equation yields $9=x$. Therefore, the value of $a$ is $9$.