Coincident lines require 1/(k − 1) = 2/(k + 1) = 3/(k + 3). Cross-multiplying the first pair gives k + 1 = 2k − 2, which solves to k = 3. This value satisfies all ratios equally.
NCERT Solution for Class 9 Ganita Manjari Part 2 chapter 13 question answer
NCERT Solution for Ganita Manjari Part 2 chapter 13 Two Variables, One Line solutions
Coincident lines represent identical equations requiring equal coefficient ratios: a₁/a₂ = b₁/b₂ = c₁/c₂. Setting up the ratios gives 1/(k − 1) = 2/(k + 1) = 3/(k + 3). Equating the first two ratios yields k + 1 = 2(k − 1), which simplifies to k = 3. Substituting k = 3 into all three ratios yields 1/2 = 2/4 = 3/6 = 1/2, confirming k = 3.
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