Line through the intersection of two lines — A/L Combined Mathematics

How do I practise Line through the intersection of two lines?

1 question with a worked solution

1. What is the equation of the straight line passing through the intersection of L₁ ≡ x + y - 4 = 0 and L₂ ≡ 2x - y - 2 = 0 and also passing through the origin (0, 0)?
   1. A) y = x
   2. B) y = 2x
   3. C) y = -x
   4. D) 2y = x
   Check my answer

   Correct answer: A) y = x

   Solving simultaneously: Adding L₁ + L₂: 3x - 6 = 0 => x = 2. From L₁: 2 + y - 4 = 0 => y = 2. Intersection point is (2, 2). The straight line passing through (0, 0) and (2, 2) has gradient m = (2 - 0)/(2 - 0) = 1, so its equation is y = x.

   Show worked solution

   Step 1: Solve L₁ and L₂: x = 2, y = 2. Step 2: Line through (0,0) and (2,2): y - 0 = (2/2)(x - 0) => y = x. Answer: y = x.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Line through the intersection of two lines fit in the syllabus?

Year 1 · Term 3