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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.
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 solRead more
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/
See lessForm a pair of linear equations and find their common solutions graphically. 10 students of Grade 9 took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
Let x denote the number of boys and y denote the number of girls. The problem yields two linear equations: x + y = 10 and y - x = 4. Plotting x + y = 10 passes through (0, 10) and (10, 0), while y - x = 4 passes through (0, 4) and (6, 10). The two straight lines intersect precisely at (3, 7), givingRead more
Let x denote the number of boys and y denote the number of girls. The problem yields two linear equations: x + y = 10 and y – x = 4. Plotting x + y = 10 passes through (0, 10) and (10, 0), while y – x = 4 passes through (0, 4) and (6, 10). The two straight lines intersect precisely at (3, 7), giving 3 boys and 7 girls.
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/
See lessA lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Let ₹x be the fixed charge for the first three days and ₹y be the charge per subsequent day. Saritha kept the book for 7 days (3 fixed + 4 extra), giving x + 4y = 27. Susy kept it for 5 days (3 fixed + 2 extra), giving x + 2y = 21. Subtracting Susy's equation from Saritha's yields 2y = 6, so y = 3.Read more
Let ₹x be the fixed charge for the first three days and ₹y be the charge per subsequent day. Saritha kept the book for 7 days (3 fixed + 4 extra), giving x + 4y = 27. Susy kept it for 5 days (3 fixed + 2 extra), giving x + 2y = 21. Subtracting Susy’s equation from Saritha’s yields 2y = 6, so y = 3. Substituting y = 3 gives x = 15. The fixed charge is ₹15 and the daily extra charge is ₹3.
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/
See lessMeena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 did she receive?
Let the number of ₹50 notes be x and the number of ₹100 notes be y. The total count of notes gives x + y = 25. The total value equation is 50x + 100y = 2000, which simplifies to x + 2y = 40 upon dividing by 50. Subtracting x + y = 25 from x + 2y = 40 yields y = 10. Substituting y = 10 gives x = 15.Read more
Let the number of ₹50 notes be x and the number of ₹100 notes be y. The total count of notes gives x + y = 25. The total value equation is 50x + 100y = 2000, which simplifies to x + 2y = 40 upon dividing by 50. Subtracting x + y = 25 from x + 2y = 40 yields y = 10. Substituting y = 10 gives x = 15. Meena received 15 ₹50 notes and 10 ₹100 notes.
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/
See lessThe sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Let the tens digit be x and the units digit be y, forming the number 10x + y. The sum of digits is x + y = 9. Reversing the digits gives 10y + x. From the second condition, 9(10x + y) = 2(10y + x), which simplifies to 90x + 9y = 20y + 2x or 88x = 11y, leading to y = 8x. Substituting into x + y = 9 gRead more
Let the tens digit be x and the units digit be y, forming the number 10x + y. The sum of digits is x + y = 9. Reversing the digits gives 10y + x. From the second condition, 9(10x + y) = 2(10y + x), which simplifies to 90x + 9y = 20y + 2x or 88x = 11y, leading to y = 8x. Substituting into x + y = 9 gives 9x = 9, so x = 1 and y = 8. The number is 18.
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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