SAT Question f03465dc: Systems of Linear Equations answer and explanation with Desmos solution

Choice A is correct. Dividing both sides of the second equation in the given system by $3$ yields $8x+7y=9$, which is the first equation in the given system. Therefore, the first and second equations represent the same line in the xy-plane. If the x- and y-coordinates of a point satisfy an equation, the point lies on the graph of the equation in the xy-plane. Choice A is a point with x-coordinate $r$ and y-coordinate $-\frac{8r}{7}+\frac{9}{7}$. Substituting $r$ for $x$ and $-\frac{8r}{7}+\frac{9}{7}$ for $y$ in the equation $8x+7y=9$ yields $8r+7\left(-\frac{8}{7}r+\frac{9}{7}\right)=9$. Applying the distributive property to the left-hand side of this equation yields $8r-8r+9=9$. Combining like terms on the left-hand side of this equation yields $9=9$, so the coordinates of the point $\left(r,-\frac{8}{7}r+\frac{9}{7}\right)$ satisfy both equations in the given system. Therefore, for each real number $r$, the point $\left(r,-\frac{8}{7}r+\frac{9}{7}\right)$ lies on the graph of each equation in the xy-plane for the given system.