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MHT CET202611 April 2026Morning ShiftMathematicsStraight LinesActual

The equation of a line passing through the point of the intersection of the lines x - y + 1 = 0 and 2x + 3y - 8 = 0 and having x intercept 3 is

Options

  1. Ax + y + 3 = 0
  2. Bx + y - 3 = 0
  3. Cx - y + 3 = 0
  4. D-x + y - 2 = 0

Correct answer

B. x + y - 3 = 0

Step-by-step solution

The given lines are: x - y + 1 = 0 2x + 3y - 8 = 0 From the first equation, y = x + 1 . Substituting this into the second equation: 2x + 3(x + 1) - 8 = 0 5x - 5 = 0 x = 1 Substituting x = 1 into y = x + 1 , we get y = 2 . The point of intersection is (1, 2) . The required line has an x-intercept of 3 , which means it passes through the point (3, 0) . The equation of the line passing through (1, 2) and (3, 0) is given by: y - 0 = 2 - 0 1 - 3 (x - 3) y = -1(x - 3) x + y - 3 = 0 Answer: x + y - 3 = 0

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