How many solutions are there to the system of equations above?

Question

Accepted Answer

Choice C is correct. The second equation of the system can be rewritten as . Substituting for y in the first equation gives . This equation can be solved as shown below: Substituting 1 for x in the equation gives . Therefore, is the only solution to the system of equations. Choice A is incorrect. In the xy -plane, a parabola and a line can intersect at no more than two points. Since the graph of the first equation is a parabola and the graph of the second equation is a line, the system cannot have more than 2 solutions. Choice B is incorrect. There is a single ordered pair that satisfies both equations of the system. Choice D is incorrect because the ordered pair satisfies both equations of the system.

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