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1. The point of intersection of the two lines is (x, y) = (- 45 / 37, – 250 / 37).

   How to find the point of intersection of two lines by vectorial methods

   Vectorially speaking, a line is represented by the following parametric expression:

   (x, y) = (a, b) + t · (c – a, d – b)        (1)

   Where:

   • (a, b) – Initial end of the line segment.
   • (c, d) – Final end of the line segment.
   • t – Parameter.

   Two points intercept each other when they share the same point (x, y). Then,

   (- 2, 5) + t₁ · (1, – 15) = (5, 15) + t₂ · (- 2, – 7)

   t₁ · (1, – 15) – t₂ · (- 2, – 7) = (7, 10)

   t₁ · (1, – 15) + t₂ · (2, 7) = (7, 10)

   Which is equivalent to the following system of linear equations:

   t₁ + 2 · t₂ = 7

   – 15 · t₁ + 7 · t₂ = 10

   Then, the solution of the system is (t₁, t₂) = (29 / 37, 115 / 37) and the point of intersection is:

   (x, y) = (- 2, 5) + (29 / 37) · (1, – 15)

   (x, y) = (- 45 / 37, – 250 / 37)

   The point of intersection of the two lines is (x, y) = (- 45 / 37, – 250 / 37).

   To learn more on systems of linear equations: https://brainly.com/question/27664510

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