A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have?
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Choice B is correct. The solutions to the system of equations are the points where the circle, parabola, and line all intersect. These points are and , and these are the only solutions to the system.
Choice A is not the correct answer. This answer may reflect the misconception that a system of equations can have only one solution.
Choice C is not the correct answer. This answer may reflect the misconception that a system of equations has as many solutions as the number of equations in the system.
Choice D is not the correct answer. This answer may reflect the misconception that the solutions of the system are represented by the points where any two of the curves intersect, rather than the correct concept that the solutions are represented only by the points where all three curves intersect.
Students must demonstrate their conceptual understanding of graphical representations of variable relationships.