This statement is True. The equation 2x + 3y = 7 can be expressed as y = (7 − 2x)/3. For any real value assigned to the independent variable x, there exists a corresponding real value for y. Because there are infinitely many real values that x can take, this linear equation in two variables possesseRead more
This statement is True. The equation 2x + 3y = 7 can be expressed as y = (7 − 2x)/3. For any real value assigned to the independent variable x, there exists a corresponding real value for y. Because there are infinitely many real values that x can take, this linear equation in two variables possesses infinitely many solutions lying along its straight-line graph.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 13 Two Variables, One Line Question Answer (2026-27)
This statement is False. An ordered pair is a solution only if substituting its coordinates makes the equation true. Substituting x = 1 and y = 2 into the left-hand side of 2x + 3y = 7 gives LHS = 2(1) + 3(2) = 2 + 6 = 8. Since LHS ≠ RHS (8 ≠ 7), the point (1, 2) does not satisfy the equation.Read more
This statement is False. An ordered pair is a solution only if substituting its coordinates makes the equation true. Substituting x = 1 and y = 2 into the left-hand side of 2x + 3y = 7 gives LHS = 2(1) + 3(2) = 2 + 6 = 8. Since LHS ≠ RHS (8 ≠ 7), the point (1, 2) does not satisfy the equation.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 13 Two Variables, One Line Question Answer (2026-27)
The two equations share the identical set of solutions because one is a non-zero multiple of the other. Dividing every term of 6x + 8y = 14 by 2 reduces it directly to 3x + 4y = 7. Because any ordered pair (x, y) that makes 3x + 4y equal to 7 will also make 2(3x + 4y) = 2(7) = 14, both represent theRead more
The two equations share the identical set of solutions because one is a non-zero multiple of the other. Dividing every term of 6x + 8y = 14 by 2 reduces it directly to 3x + 4y = 7. Because any ordered pair (x, y) that makes 3x + 4y equal to 7 will also make 2(3x + 4y) = 2(7) = 14, both represent the exact same line and solution set.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 13 Two Variables, One Line Question Answer (2026-27)
Let (u, v) be any solution to ax + by = c, meaning au + bv = c holds true. Multiplying both sides by a non-zero constant k yields k(au + bv) = kc or kax + kby = kc, proving that (u, v) satisfies the second equation. Conversely, dividing the second equation by k ≠ 0 restores the first, showing that bRead more
Let (u, v) be any solution to ax + by = c, meaning au + bv = c holds true. Multiplying both sides by a non-zero constant k yields k(au + bv) = kc or kax + kby = kc, proving that (u, v) satisfies the second equation. Conversely, dividing the second equation by k ≠ 0 restores the first, showing that both equations describe identical solution sets.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 13 Two Variables, One Line Question Answer (2026-27)
For (i): (a) Yes, sticks must be equal because every quadrilateral in Q has equal-length diagonals. (b) Yes, how they are joined matters; equal diagonals are necessary but not sufficient to ensure the shape belongs to Q. For (ii): (a) Yes, sticks must be equal. (b) No, it will not matter how they crRead more
For (i): (a) Yes, sticks must be equal because every quadrilateral in Q has equal-length diagonals. (b) Yes, how they are joined matters; equal diagonals are necessary but not sufficient to ensure the shape belongs to Q. For (ii): (a) Yes, sticks must be equal. (b) No, it will not matter how they cross, because any quadrilateral with equal diagonals automatically belongs to Q.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
The equation 2x + 3y = 7 has infinitely many solutions.
This statement is True. The equation 2x + 3y = 7 can be expressed as y = (7 − 2x)/3. For any real value assigned to the independent variable x, there exists a corresponding real value for y. Because there are infinitely many real values that x can take, this linear equation in two variables possesseRead more
This statement is True. The equation 2x + 3y = 7 can be expressed as y = (7 − 2x)/3. For any real value assigned to the independent variable x, there exists a corresponding real value for y. Because there are infinitely many real values that x can take, this linear equation in two variables possesses infinitely many solutions lying along its straight-line graph.
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 point (1, 2) is a solution of the equation 2x + 3y = 7.
This statement is False. An ordered pair is a solution only if substituting its coordinates makes the equation true. Substituting x = 1 and y = 2 into the left-hand side of 2x + 3y = 7 gives LHS = 2(1) + 3(2) = 2 + 6 = 8. Since LHS ≠ RHS (8 ≠ 7), the point (1, 2) does not satisfy the equation.Read more
This statement is False. An ordered pair is a solution only if substituting its coordinates makes the equation true. Substituting x = 1 and y = 2 into the left-hand side of 2x + 3y = 7 gives LHS = 2(1) + 3(2) = 2 + 6 = 8. Since LHS ≠ RHS (8 ≠ 7), the point (1, 2) does not satisfy the equation.
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 lessCompare the solutions of the equations 3x + 4y = 7 and 6x + 8y = 14. Argue that they have the same set of solutions, that is, every solution of one is also a solution of the other.
The two equations share the identical set of solutions because one is a non-zero multiple of the other. Dividing every term of 6x + 8y = 14 by 2 reduces it directly to 3x + 4y = 7. Because any ordered pair (x, y) that makes 3x + 4y equal to 7 will also make 2(3x + 4y) = 2(7) = 14, both represent theRead more
The two equations share the identical set of solutions because one is a non-zero multiple of the other. Dividing every term of 6x + 8y = 14 by 2 reduces it directly to 3x + 4y = 7. Because any ordered pair (x, y) that makes 3x + 4y equal to 7 will also make 2(3x + 4y) = 2(7) = 14, both represent the exact same line and solution set.
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 lessShow that the equations ax + by = c and kax + kby = kc, with k ≠ 0, have the same set of solutions.
Let (u, v) be any solution to ax + by = c, meaning au + bv = c holds true. Multiplying both sides by a non-zero constant k yields k(au + bv) = kc or kax + kby = kc, proving that (u, v) satisfies the second equation. Conversely, dividing the second equation by k ≠ 0 restores the first, showing that bRead more
Let (u, v) be any solution to ax + by = c, meaning au + bv = c holds true. Multiplying both sides by a non-zero constant k yields k(au + bv) = kc or kax + kby = kc, proving that (u, v) satisfies the second equation. Conversely, dividing the second equation by k ≠ 0 restores the first, showing that both equations describe identical solution sets.
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 lessWe have identified different types of quadrilaterals—squares, rectangles, parallelograms, rhombi, kites and trapezia. One can identify more types (e.g., we could create a category of quadrilaterals that have equal-length opposite sides). Suppose we have identified a category of quadrilaterals called Q and we have to construct a quadrilateral of this type. For this, we are to use two thin sticks, put them together as diagonals so that the quadrilateral obtained by joining their endpoints is of type Q (see the Fig. 9.2). (i) Suppose Q satisfies the following property. If a quadrilateral is of type Q, then it has equal-length diagonals. (a) Should the two sticks be of equal length? Why or why not? (b) Will it matter how the two sticks are put together? (ii) Instead of the property mentioned above, suppose Q satisfies the following property. If a quadrilateral has equal diagonals, then it is of type Q. What will be your answers to (a) and (b) now?
For (i): (a) Yes, sticks must be equal because every quadrilateral in Q has equal-length diagonals. (b) Yes, how they are joined matters; equal diagonals are necessary but not sufficient to ensure the shape belongs to Q. For (ii): (a) Yes, sticks must be equal. (b) No, it will not matter how they crRead more
For (i): (a) Yes, sticks must be equal because every quadrilateral in Q has equal-length diagonals. (b) Yes, how they are joined matters; equal diagonals are necessary but not sufficient to ensure the shape belongs to Q. For (ii): (a) Yes, sticks must be equal. (b) No, it will not matter how they cross, because any quadrilateral with equal diagonals automatically belongs to Q.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See less