SAT Question 8383771a: Systems of Linear Equations answer and explanation with Desmos solution

Choice A is incorrect. The equation $3x+3y=60$ can be rewritten as $x+y=20$. Since $x+y=20$ is the same as the given equation, the system of $3x+3y=60$ and $x+y=20$ has infinitely many solutions rather than exactly one solution.

Choice B is incorrect. The equation $-x-y=40$ can be rewritten as $x+y=-40$. The graph of this line has a slope of $-1$. Since the graphs of the lines represented by the equations $x+y=-40$ and $x+y=20$ have the same slope in the xy-plane and the equations aren't equivalent, this system has no solution rather than exactly one solution.

Choice C is incorrect. The equation $3x+3y=14$ can be rewritten as $x+y=\frac{14}{3}$. The graph of this line has a slope of $-1$. Since the graphs of the lines represented by the equations $x+y=\frac{14}{3}$ and $x+y=20$ have the same slope in the xy-plane and the equations aren't equivalent, this system has no solution rather than exactly one solution.