If 3^(x + y) = 81 and 2^(2x - y) = 32, what is the value of x y?

Answer and explanation

Correct answer: B. 3

  1. Step 1: Since 81 = 3^4, x + y = 4.
  2. Step 2: Since 32 = 2^5, 2*x - y = 5.
  3. Step 3: Add the two linear equations: (x + y) + (2x - y) = 4 + 5, so 3x = 9, giving x = 3.
  4. Step 4: Substitute into first equation: 3 + y = 4, so y = 1.
  5. Step 5: Product x y = 3 1 = 3.
Answer
3.
Why not the others: 4 is the sum x + y; 2 computes x - y; 6 computes 2 * x.

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