In the equation above, and are constants. If the equation has infinitely many solutions, what are the values of and ?
Explanation
Choice B is correct. Distributing the a on the left-hand side of the equation gives . Rearranging the terms in each side of the equation yields . Since the equation has infinitely many solutions, it follows that the coefficients of x and the free terms on both sides must be equal. That is, , or , and Substituting 2 for a in the equation gives , so .
Choice A is incorrect and may be the result of a conceptual error when finding the value of b. Choices C and D are incorrect and may result from making a sign error when simplifying.