SAT Question e77a76ce: Systems of Linear Equations answer and explanation with Desmos solution

Choice A is correct. A system of two linear equations in two variables, $x$ and $y$, has no solution if the graphs of the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by equations in slope-intercept form, $y=mx+b$, where $m$ and $b$ are constants, are parallel if their slopes, $m$, are the same and are distinct if their y-coordinates of the y-intercepts, $b$, are different. In the equations $y=6x+3$ and $y=6x+9$, the values of $m$ are each $6$, and the values of $b$ are $3$ and $9$, respectively. Since the slopes of these lines are the same and the y-coordinates of the y-intercepts are different, it follows that the system of linear equations in choice A has no solution.