SAT Math Multiple Choice Question 185: Answer and Explanation

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Question: 185

5. 2s - t = 10
5s = t + 12 - s

Which of the following is a true statement about the system of equations above?

  • A. There are infinitely many solutions to the system of equations.
  • B. When the system is solved for s, the result is 5.
  • C. When the system is solved for t, the result is 6.
  • D. There are no solutions to the system of equations.

Correct Answer: D

Explanation:

D The first step is to rewrite the bottom equation so that it is in the same format as the first equation. Move all of the variables in the bottom equation to the left side of the equation to get 6s - t = 12. If the answer is (A) and there are infinitely many solutions to the system of equations, then the two equations must be the same equation. To determine whether this is the case, multiply the top equation through by 3 to get 6s - t = 30. Since it cannot be the case that the equation 6s - t equals both 12 and 30, the correct answer is (D). There are no solutions to the system of equations.

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