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WAEC 2024 Mathematics · Question 16

If 3x - 2y = - 5 and x + 2y = 9, find the value of x−yx+y\frac{x - y}{x + y}

Options

  1. A.53\frac{5}{3}
  2. B.35\frac{3}{5}
  3. C.−35\frac{-3}{5}
  4. D.−53\frac{-5}{3}

Answer: C. −35\frac{-3}{5}

Explanation written with AI and checked against the answer key

Analyze the question: We have two simultaneous equations. We must find x and y, then evaluate (x − y)/(x + y). Concept: Use elimination. The y-terms (−2y and +2y) cancel when we add the equations. Solution: Equation 1: 3x − 2y = −5 Equation 2: x + 2y = 9 Add them: 4x = 4 x = 1 Substitute x = 1 into Equation 2: 1 + 2y = 9 2y = 8 y = 4 Check in Equation 1: 3(1) − 2(4) = 3 − 8 = −5 ✓ Now evaluate: (x − y)/(x + y) = (1 − 4)/(1 + 4) = −3/5 Answer: −3/5, which is option C. Tip: When the coefficients of one variable are opposites (like −2y and +2y), just add the equations straight away. Always substitute back into the other equation to verify your values before computing the final expression.

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