In the equation above, a and b are constants. If the equation has infinitely many solutions, what are the values

Question

In the equation above, a and b are constants. If the equation has infinitely many solutions, what are the values of a and b ?

Accepted Answer

Choice B is correct. Distributing the a on the left-hand side of the equation gives 3 a - b - ax = -1 - 2 x . Rearranging the terms in each side of the equation yields - ax + 3 a - b = -2 x -1. 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, - a = -2, or a = 2, and 3 a - b = -1. Substituting 2 for a in the equation 3 a - b = -1 gives 3(2) - b = -1, so b = 7. 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.

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