The point of intersection of the two lines is (x, y) = (- 45 / 37, - 250 / 37).
Vectorially speaking, a line is represented by the following parametric expression:
(x, y) = (a, b) + t · (c - a, d - b) (1)
Where:
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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