If is a solution to the system of equations above, which of the following is a possible value of x

Question

If is a solution to the system of equations above, which of the following is a possible value of x ?

Accepted Answer

Choice D is correct. Substituting from the second equation for y in the first equation yields . Subtracting 12 from both sides of this equation and rewriting the equation results in . Factoring the left-hand side of this equation yields . Using the zero product property to solve for x , it follows that and . Solving each equation for x yields and , respectively. Thus, two possible values of x are 3 and . Of the choices given, 3 is the only possible value of x . Choices A, B, and C are incorrect. Substituting 0 for x in the first equation gives , or ; then, substituting 12 for y and 0 for x in the second equation gives , or , which is false. Similarly, substituting 1 or 2 for x in the first equation yields or , respectively; then, substituting 11 or 10 for y in the second equation yields a false statement.

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