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MHT CET202522 Apr 2025Morning ShiftMathematicsPair of LinesActual

If the pair of straight lines x y-x+y-1=0 and the line x+ ky -3=0 are concurrent, then the value of k is equal to

Options

  1. A4
  2. B3
  3. C-1
  4. D2

Correct answer

A. 4

Step-by-step solution

The given equation xy - x + y - 1 = 0 factors as (x+1)(y-1) = 0 , which represents the lines x = -1 and y = 1 , intersecting at (-1, 1) . For the line x + ky - 3 = 0 to be concurrent with these lines, the point (-1, 1) must satisfy its equation: (-1) + k(1) - 3 = 0 k - 4 = 0 k = 4 The value is A .

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