A
B
C
D
Explanation
Correct answer: C.
Choice C is correct. The solutions to a system of two equations correspond to points where the graphs of the equations intersect. The given graphs intersect at points; therefore, the system has solutions.
Desmos solution:
Note: Count the intersection points of the blue parabola and green line to find the number of solutions.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect because the graphs intersect.
Choice B
Choice B is incorrect because the graphs intersect more than once.
Choice D
Choice D is incorrect. It's not possible for the graph of a quadratic equation and the graph of a linear equation to intersect more than twice.