Based on the system of equations above, what is the value of the product xy?
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Choice C is correct. There are several solution methods possible, but all involve persevering in solving for the two variables and calculating the product. For example, combining like terms in the first equation yields and then multiplying that by 2 gives When this transformed equation is added to the second given equation, the y-terms are eliminated, leaving an equation in just one variable: or Substituting 2 for x in the second equation (one could use either to solve) yields which gives Finally, the product xy is
Choice A is not the correct answer. Students who select this option have most likely made a calculation error in transforming the second equation (using instead of ) and used it to eliminate the x-terms.
Choice B is not the correct answer. This is the value of y for the solution of the system, but it has not been put back into the system to solve for x to determine the product xy.
Choice D is not the correct answer. Not understanding how to eliminate a variable when solving a system, a student may have added the equations and to yield . From here, a student may mistakenly simplify the left-hand side of this resulting equation to yield and then proceed to use division by 9 on both sides in order to solve for xy.
Students must solve a system of linear equations.