Solve the non-linear simultaneous system: y = x^2 - 3x - 4 and y = 2x + 2. What are the points of intersection?
Answer and explanation
Correct answer: C. (-1, 0) and (6, 14)
- Step 1: Step 1: Equate the equations: x^2 - 3x - 4 = 2x + 2 => x^2 - 5x - 6 = 0. Factorise: (x - 6)(x + 1) = 0 => x = 6 or x = -1. Step 2. Step 2: Find corresponding y values using y = 2x + 2: For x = 6, y = 2(6) + 2 = 14; for x = -1, y = 2(-1) + 2 = 0. Points are (6, 14) and (-1, 0). Answer: (-1, 0) and (6, 14). Why not the others: Sign errors produce x = 1 and x = -6, leading to false intersection points.
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