SAT Question e2e3942f: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. A system of two linear equations has no solution when the graphs of the equations have the same slope and different $y$-coordinates of the $y$-intercepts. Each of the given equations is written in the slope-intercept form of a linear equation, $y=mx+b$, where $m$ is the slope and $b$ is the $y$-coordinate of the $y$-intercept of the graph of the equation. For these two linear equations, the $y$-coordinates of the $y$-intercepts are different: $1$ and $-8$. Thus, if the system of equations has no solution, the slopes of the two linear equations must be the same. The slope of the first linear equation is $2$. Therefore, for the system of equations to have no solution, the value of $a$ must be $2$.