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Use the ratios a₁/a₂, b₁/b₂, c₁/c₂ to determine whether the lines representing 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0 intersect at a point, are parallel or are coincident.

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Here, a₁/a₂ = 5/7 and b₁/b₂ = -4/6 = -2/3. Since a₁/a₂ ≠ b₁/b₂, the system possesses a unique solution, meaning the lines intersect at a single point.

Class 9 Maths (Ganita Manjari part two) Chapter 13 questions answer
Class 9 Maths (Ganita Manjari part two) Two Variables, One Line Question Answer

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  1. Comparing the coefficients with the standard form gives a₁ = 5, b₁ = -4, c₁ = 8 and a₂ = 7, b₂ = 6, c₂ = -9. Computing the ratios yields a₁/a₂ = 5/7 and b₁/b₂ = -4/6 = -2/3. Because a₁/a₂ ≠ b₁/b₂, the lines have different slopes and therefore intersect at exactly one point, representing a unique solution.

     

    For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 13 Two Variables, One Line Question Answer (2026-27)

    https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-13/

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