SAT Question 36f068e2: Systems of Linear Equations answer and explanation with Desmos solution

Choice B is correct. The intercepts of the graph of each equation can be found by substituting $0$ for one variable at a time. For the equation $x+y=53$, substituting $0$ for $y$ yields $x=53$, so the x-intercept of the graph of the equation is $(53,0)$. Substituting $0$ for $x$ in this equation yields $y=53$, so the y-intercept of the graph of the equation is $(0,53)$. Thus, the graph of the equation $x+y=53$ has intercepts at $(53,0)$ and $(0,53)$. For the equation $11x+18y=730$, substituting $0$ for $y$ yields $x=\frac{730}{11}$, so the x-intercept of the graph of the equation is approximately $(66,0)$. Substituting $0$ for $x$ in this equation yields $y=\frac{730}{18}$, so the y-intercept of the graph of the equation is approximately $(0,41)$. Thus, the graph of the equation $11x+18y=730$ has intercepts at approximately $(66,0)$ and $(0,41)$. Choice B is a graph that shows one line with intercepts at $(0,53)$ and $(53,0)$ and another line with intercepts at approximately $(0,41)$ and $(66,0)$. Thus, choice B represents this situation.