OG详解-OG4 数学2 Q22

Choice A is correct. A solution to a system of equations must satisfy each equation in the system. It follows that if an ordered pair  (x, y) is a solution to the system, the point  (x, y) lies on the graph in the xy-plane of each equation in the system. The only point that lies on each graph of the system of two linear equations shown is their intersection point  (8, 2). It follows that if a new graph of three linear equations is created using the system of equations shown and the graph of x + 4y =-16, this system has either zero solutions or one solution, the point (8, 2). Substituting  8 for x  and 2  for y  in the equation x + 4y =-16 yields 8 + 4(2)=-16, or 16 =-16. Since this equation is not true, the point  (8, 2) does not lie on the graph f x + 4y =-16. Therefore, (8, 2) is not a solution to the system of three equations. It follows that there are zero solutions to this system.
Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.