SAT Question 6a87902f: 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 zero points of intersection if 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, $y=mx+b$, are distinct if the y-coordinates of their y-intercepts, $b$, are different and are parallel if their slopes, $m$, are the same. For the two equations in the given system, $y=2x+10$ and $y=2x-1$, the values of $b$ are $10$ and $-1$, respectively, and the values of $m$ are both $2$. Since the values of $b$ are different, the graphs of these lines have different y-coordinates of the y-intercept and are distinct. Since the values of $m$ are the same, the graphs of these lines have the same slope and are parallel. Therefore, the graphs of the given equations are lines that intersect at zero points in the xy-plane.