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JAMB 2016 Mathematics · Question 41

Solve for x and y respectively 3x - 5y = 9 6x - 4y = 12

Options

  1. A.34\frac{3}{4}, 1
  2. B.43\frac{4}{3}, 1
  3. C.34\frac{3}{4}, -1
  4. D.43\frac{4}{3}, -1

Answer: D. 43\frac{4}{3}, -1

Explanation written with AI and checked against the answer key

Analyze the question: We have two linear equations in two unknowns and need to find x and y. 3x − 5y = 9 ... (1) 6x − 4y = 12 ... (2) Concept: Use elimination. Make the coefficients of x equal, then subtract. Solution: Multiply (1) by 2: 6x − 10y = 18 ... (3) Subtract (3) from (2): (6x − 4y) − (6x − 10y) = 12 − 18 6y = −6 y = −1 Substitute y = −1 into (1): 3x − 5(−1) = 9 3x + 5 = 9 3x = 4 x = 4/3 Check in (2): 6(4/3) − 4(−1) = 8 + 4 = 12 ✓ Check in (1): 3(4/3) − 5(−1) = 4 + 5 = 9 ✓ Tip: In simultaneous equations, when one equation's coefficients are a multiple of the other's (here 3 → 6), multiply to match one variable and subtract. Always plug your answers back into both equations. It takes seconds and confirms the answer in the exam.

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