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Which of the following pairs of linear equations have solutions? If they have solutions, find them graphically: 2x + y – 6 = 0, 4x – 2y – 4 = 0.
This system has a unique solution because a₁/a₂ = 2/4 = 1/2 while b₁/b₂ = 1/(-2) = -1/2, satisfying a₁/a₂ ≠ b₁/b₂. The line 2x + y = 6 passes through (0, 6) and (3, 0), while 4x - 2y = 4 passes through (0, -2) and (1, 0). Plotting them on graph paper shows their intersection occurs at (2, 2), whichRead more
This system has a unique solution because a₁/a₂ = 2/4 = 1/2 while b₁/b₂ = 1/(-2) = -1/2, satisfying a₁/a₂ ≠ b₁/b₂. The line 2x + y = 6 passes through (0, 6) and (3, 0), while 4x – 2y = 4 passes through (0, -2) and (1, 0). Plotting them on graph paper shows their intersection occurs at (2, 2), which is the common 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 lessWhich of the following pairs of linear equations have solutions? If they have solutions, find them graphically: x – y = 8, 3x – 3y = 16.
This pair of equations has no solution. Evaluating the ratios gives a₁/a₂ = 1/3, b₁/b₂ = 1/3 and c₁/c₂ = 1/2. Because a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines share the exact same slope of 1 but possess different y-intercepts. When plotted on a Cartesian plane, they form two distinct parallel lines that nevRead more
This pair of equations has no solution. Evaluating the ratios gives a₁/a₂ = 1/3, b₁/b₂ = 1/3 and c₁/c₂ = 1/2. Because a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines share the exact same slope of 1 but possess different y-intercepts. When plotted on a Cartesian plane, they form two distinct parallel lines that never cross, leaving zero common points.
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: x + y = 5, 2x + 2y = 10.
This pair has infinitely many solutions. The coefficient ratios are a₁/a₂ = 1/2, b₁/b₂ = 1/2 and c₁/c₂ = -5/(-10) = 1/2. Since all ratios are equal, the graphs coincide into a single line passing through (0, 5) and (5, 0). Therefore, every coordinate pair satisfying x + y = 5, such as (1, 4) or (2,Read more
This pair has infinitely many solutions. The coefficient ratios are a₁/a₂ = 1/2, b₁/b₂ = 1/2 and c₁/c₂ = -5/(-10) = 1/2. Since all ratios are equal, the graphs coincide into a single line passing through (0, 5) and (5, 0). Therefore, every coordinate pair satisfying x + y = 5, such as (1, 4) or (2, 3), is a valid graphical 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 lessUse the ratios a₁/a₂, b₁/b₂, c₁/c₂ to determine whether the lines representing 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0 intersect at a point, are parallel or are coincident.
From the equations, we identify the coefficients as a₁ = 9, b₁ = 3, c₁ = 12 and a₂ = 18, b₂ = 6, c₂ = 24. Calculating the ratios produces a₁/a₂ = 1/2, b₁/b₂ = 1/2 and c₁/c₂ = 1/2. Since a₁/a₂ = b₁/b₂ = c₁/c₂, the two equations represent the exact same line geometrically, which means the lines are coRead more
From the equations, we identify the coefficients as a₁ = 9, b₁ = 3, c₁ = 12 and a₂ = 18, b₂ = 6, c₂ = 24. Calculating the ratios produces a₁/a₂ = 1/2, b₁/b₂ = 1/2 and c₁/c₂ = 1/2. Since a₁/a₂ = b₁/b₂ = c₁/c₂, the two equations represent the exact same line geometrically, which means the lines are coincident.
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 lessUse the ratios a₁/a₂, b₁/b₂, c₁/c₂ to determine whether the lines representing 6x – 3y + 10 = 0 and 2x – y + 9 = 0 intersect at a point, are parallel or are coincident.
Comparing the coefficients with the standard form gives a₁ = 6, b₁ = -3, c₁ = 10 and a₂ = 2, b₂ = -1, c₂ = 9. We find that a₁/a₂ = 3, b₁/b₂ = 3, but c₁/c₂ = 10/9. Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, both lines have identical slopes but different intercepts, making them strictly parallel without any interseRead more
Comparing the coefficients with the standard form gives a₁ = 6, b₁ = -3, c₁ = 10 and a₂ = 2, b₂ = -1, c₂ = 9. We find that a₁/a₂ = 3, b₁/b₂ = 3, but c₁/c₂ = 10/9. Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, both lines have identical slopes but different intercepts, making them strictly parallel without any intersection point.
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