The equation , where a and b are constants, has no solutions. Which of the following must be true? I.

Question

The equation , where a and b are constants, has no solutions. Which of the following must be true? I. II. III.

Accepted Answer

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 we must be true. Inspecting the remaining terms, 5 can&rsquo;t equal . Dividing both of these quantities by 9 yields that b can&rsquo;t equal . Therefore, statement IIwe must be true. Since b can have any value other than , statement Iwe 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&rsquo;t required to be 5.

Question the-eq