HardMath· Advanced Math· Nonlinear equations in one variable and systems of equations in two variables· MCQ
How many solutions are there to the system of equations above?
A
There are exactly 4 solutions.
B
There are exactly 2 solutions.
C
There is exactly 1 solution.
D
There are no solutions.
Correct answer: C
Explanation
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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id cb_question_bank:cb007c32-1efa-4b00-8925-75c80e21fce8 · question 2c5c22d0 · IBN 09411-DC
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