SAT Question 75012ee7: Systems of Linear Equations answer and explanation with Desmos solution

Choice B is correct. The two given equations are equivalent because the second equation can be obtained from the first equation by multiplying each side of the equation by $5$. Thus, the graphs of the equations are coincident, so if a point lies on the graph of one of the equations, it also lies on the graph of the other equation. A point $\left(x,y\right)$ lies on the graph of an equation in the xy-plane if and only if this point represents a solution to the equation. It is sufficient, therefore, to find the point that represents a solution to the first given equation. Substituting the x- and y-coordinates of choice B, $-\frac{3r}{2}+\frac{7}{2}$ and $r$, for $x$ and $y$, respectively, in the first equation yields $2\left(-\frac{3r}{2}+\frac{7}{2}\right)+3r=7$, which is equivalent to $-3r+7+3r=7$, or $7=7$. Therefore, the point $\left(-\frac{3r}{2}+\frac{7}{2},r\right)$ represents a solution to the first equation and thus lies on the graph of each equation in the xy-plane for the given system.