SAT Question 6e6a3241: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. The graph of a system of equations is the graph that shows the lines represented by each of the equations in the system. The $x$-intercept of the graph of each given equation can be found by substituting $0$ for $y$ in each equation: $x+5\times 0=5$, or $x=5$, and $2x-0=-4$, or $x=-2$. The $y$-intercept of the graph of each equation can be found by substituting $0$ for $x$ in each equation: $0+5y=5$, or $y=1$, and $2\times 0-y=-4$ or $y=4$. Using these $x$- and $y$-intercept values, the line that has equation $x+5y=5$ passes through the points $(0,1)$ and $(5,0)$, and the line that has equation $2x-y=-4$ passes through the points $(0,4)$ and $(-2,0)$. Only the lines in choice C pass through these points and can be used to solve the given system of equations.