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5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of each pencil and pen.
Let the cost of a pencil be ₹x and a pen be ₹y. The given relations are 5x + 7y = 50 and 7x + 5y = 46. Adding both equations yields 12x + 12y = 96, which simplifies to x + y = 8. Subtracting the first equation from the second yields 2x − 2y = −4 or x − y = −2. Adding these simplified equations givesRead more
Let the cost of a pencil be ₹x and a pen be ₹y. The given relations are 5x + 7y = 50 and 7x + 5y = 46. Adding both equations yields 12x + 12y = 96, which simplifies to x + y = 8. Subtracting the first equation from the second yields 2x − 2y = −4 or x − y = −2. Adding these simplified equations gives 2x = 6, so x = 3 and y = 5.
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 lessHere is a problem that was posed by Mahāvīrāchārya in Gaṇita sāra saṅgraha (c. 850 CE). The price of 9 citrons and 7 fragrant wood-apples taken together is 107; and the price of 7 citrons and 9 fragrant wood-apples taken together is 101. O mathematician, tell me quickly the price of each citron and of each fragrant wood-apple.
Letting the citron price be x and wood-apple price be y gives 9x + 7y = 107 and 7x + 9y = 101. Because the coefficients are interchanged, adding the two equations yields 16x + 16y = 208, which simplifies to x + y = 13. Subtracting them yields 2x − 2y = 6, giving x − y = 3. Solving these two simplerRead more
Letting the citron price be x and wood-apple price be y gives 9x + 7y = 107 and 7x + 9y = 101. Because the coefficients are interchanged, adding the two equations yields 16x + 16y = 208, which simplifies to x + y = 13. Subtracting them yields 2x − 2y = 6, giving x − y = 3. Solving these two simpler equations gives x = 8 and y = 5.
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 lessGiven the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables so that the graphs of the pair formed represent (i) intersecting lines (ii) parallel lines (iii) coincident lines.
For intersecting lines, ratios of coefficients must differ; choosing 3x + 2y - 9 = 0 satisfies a₁/a₂ ≠ b₁/b₂ as 2/3 ≠ 3/2. For parallel lines, variable ratios must match while constants differ; choosing 2x + 3y - 12 = 0 gives 2/2 = 3/3 ≠ -8/(-12). For coincident lines, all ratios must match; multiplRead more
For intersecting lines, ratios of coefficients must differ; choosing 3x + 2y – 9 = 0 satisfies a₁/a₂ ≠ b₁/b₂ as 2/3 ≠ 3/2. For parallel lines, variable ratios must match while constants differ; choosing 2x + 3y – 12 = 0 gives 2/2 = 3/3 ≠ -8/(-12). For coincident lines, all ratios must match; multiplying by 2 yields 4x + 6y – 16 = 0, satisfying a₁/a₂ = b₁/b₂ = c₁/c₂.
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 lessHalf the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
perimeter gives x + y = 36. Since length exceeds width by 4 m, x - y = 4. Adding both equations eliminates y to give 2x = 40, meaning x = 20 metres. Consequently, y = 20 - 4 = 16 metres. The garden is 20 m long and 16 m wide. For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 ChaRead more
perimeter gives x + y = 36. Since length exceeds width by 4 m, x – y = 4. Adding both equations eliminates y to give 2x = 40, meaning x = 20 metres. Consequently, y = 20 – 4 = 16 metres. The garden is 20 m long and 16 m wide.
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 lessWhich of the following pairs of linear equations have solutions? If they have solutions, find them graphically: 2x – 2y – 2 = 0, 4x – 4y – 5 = 0.
This system has no solution. The ratios are a₁/a₂ = 2/4 = 1/2, b₁/b₂ = -2/(-4) = 1/2 and c₁/c₂ = -2/(-5) = 2/5. Because a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel. Plotting x - y = 1 through (1, 0), (0, -1) and 4x - 4y = 5 through (1.25, 0), (0, -1.25) demonstrates that they never meet anywhere oRead more
This system has no solution. The ratios are a₁/a₂ = 2/4 = 1/2, b₁/b₂ = -2/(-4) = 1/2 and c₁/c₂ = -2/(-5) = 2/5. Because a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel. Plotting x – y = 1 through (1, 0), (0, -1) and 4x – 4y = 5 through (1.25, 0), (0, -1.25) demonstrates that they never meet anywhere on the coordinate plane.
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 less