SAT Math Multiple Choice Question 144: Answer and Explanation

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Question: 144

9. If 8x + 8y = 18 and x2 - y2 = - , what is the value of 2x - 2y ?

  • A. -
  • B. -
  • C.
  • D.

Correct Answer: A

Explanation:

A Start by simplifying 8x + 8y = 18 by dividing each term by 8: x + y = or : x + y = . The second equation provided in the question can be factored: x2 - y2 is the same as (x + y)(x - y), so the second equation can also be written (x + y)(x - y) = -. Since you know that x + y = , you can rewrite the second equation as (x - y) = -. Multiply both sides by : : x - y = -() or x - y = -. Since the question asks for the value of 2x - 2y, simply multiply everything by 2: 2(x - y) = 2(-) = -, which is (A).

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