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MissTica
2 years ago
14

3. Consider the straight line x + y = 1 and the family of straight lines that pass

Mathematics
1 answer:
ANTONII [103]2 years ago
5 0

Answer:

  • solution: (1/(1+m), m/(1+m))
  • no solution for m = -1 (lines are parallel)

Step-by-step explanation:

Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.

The solution to the system can be found by substitution:

  x +mx = 1

  x(1 +m) = 1 . . . . factor out x

  x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1

  y = m/(1+m) . . . . find the y-coordinate of the solution

The point of intersection is (1/(1+m), m/(1+m)).

__

The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.

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