sat suite question viewer
For each real number , which of the following points lies on the graph of each equation in the xy-plane for the given system?
Explanation
Choice A is correct. Dividing both sides of the second equation in the given system by yields , which is the first equation in the given system. Therefore, the first and second equations represent the same line in the xy-plane. If the x- and y-coordinates of a point satisfy an equation, the point lies on the graph of the equation in the xy-plane. Choice A is a point with x-coordinate and y-coordinate . Substituting for and for in the equation yields . Applying the distributive property to the left-hand side of this equation yields . Combining like terms on the left-hand side of this equation yields , so the coordinates of the point satisfy both equations in the given system. Therefore, for each real number , the point lies on the graph of each equation in the xy-plane for the given 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.