HardMath· Algebra· Linear equations in one variable· MCQ
The equation , where a and b are constants, has no solutions. Which of the following must be true?
I.
II.
III.
A
None
B
I only
C
I and II only
D
I and III only
Correct answer: D
Explanation
Choice D is correct. For a linear equation in a form to have no solutions, the x-terms must have equal coefficients and the remaining terms must not be equal. Expanding the right-hand side of the given equation yields . Inspecting the x-terms, 9 must equal a, so statement I must be true. Inspecting the remaining terms, 5 can’t equal . Dividing both of these quantities by 9 yields that b can’t equal . Therefore, statement III must be true. Since b can have any value other than , statement II may or may not be true.
Choice A is incorrect. For the given equation to have no solution, both and must be true. Choice B is incorrect because it must also be true that . Choice C is incorrect because when , there are many values of b that lead to an equation having no solution. That is, b might be 5, but b isn’t required to be 5.
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id cb_question_bank:d443ef51-d0b2-4400-97aa-26776aeb1637 · question 3f8a701b · IBN 10864-DC
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