Solve the simultaneous system of linear and quadratic equations: y = x + 1 and x² + y² = 13 for positive x and y.
Answer and explanation
Correct answer: A. x = 2, y = 3
- Step 1: Substitute y into quadratic: x² + (x + 1)² = 13. Step 2. Expand: x² + x² + 2x + 1 = 13 => 2x² + 2x - 12 = 0. Step 3. Divide by 2: x² + x - 6 = 0 => (x + 3)(x - 2) = 0. Step 4. Since x > 0, x = 2. Then y = 2 + 1 = 3. Check: 2² + 3² = 4 + 9 = 13. Answer: x = 2, y = 3. Why not the others: x = 3, y = 4 gives 3² + 4² = 25 ≠ 13; x = 1, y = 2 gives 1 + 4 = 5 ≠ 13; x = 4, y = 5 gives 41 ≠ 13.
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