# NCERT Solutions for Class 9 Maths Chapter 4

Free download NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1, 4.2, 4.3 and 4.4 of Linear Equations in two variables in English Medium and Hindi Medium free to use . Class 9 Maths NCERT Solutions for all chapter are given to download. These solutions are prepared as per latest CBSE Curriculum for 2020 – 2021 Exams.

## NCERT Solutions for Class 9 Maths Chapter 4

If you need solutions in Hindi, Click for Hindi Medium solutions of 9 Maths Chapter 4

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### 9 Maths Chapter 4 All Exercises in Hindi

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Next Chapter: Chapter 5

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##### Class 9 Maths Chapter 4 – Linear Equations in two Variables
###### Important Questions with Answers for Practice
1. The graph of the linear equation 4x = 6 is parallel to which axis. [Answer: y – axis]
2. Point (a, 0) lie on which axis? [Answer: x – axis]
3. Write the equation of x axis. [Answer: y = 0]
4. In a Residential society, Rain water is stored in underground water tank. If the water stored at the rate of 30 cubic cm per second. If water store in ‘x’ seconds and ‘y’ cubic cm. (i) Write this statement in linear equation in two variables. (ii) Write this equation in the form of ax + by + c = 0. (iii) What value of the society members shows in Rain water storage? [Answer: (i) y = 30 x, (ii) 30 x – y + 0 = 0, (iii) Environmental concerned and Cooperation]
5. Write a linear equation of two variables for x = 5, y = -2. [Answer: 2x – y = 12]
6. Find the value of K, if x = 1, y = – 1 is a solution of equation Kx – 2y = 0. [Answer: k = – 2]
7. Write the linear equation which is parallel to x-axis and is at a distance of 2 units from the origin in upward direction. [Answer: y = 2]
8. How many solutions are there for equation y = 5x + 2. [Answer: Infinite many solutions]
9. Write the equation 5y=9 as linear equation in two variables. [Answer: 0x + 5y = 9]
10. If the graph of equation 2x + Ky = 10k intersects x axis at point (5, 0) find the value of K. [Answer: k = 1]
11. Express x in terms of y for the equation 3x + 4y = 7. [Answer: x = (7 – 4y)/3]
12. Write the equations of two lines passing through (3, 10). [Answer: x + y = 13, 4x – y = 2]
13. Write the coordinates of the point where the graph of the equation 5x + 2y = 10 intersect both the axes. [Answer: (0, 5) and (2, 0)]
14. If the points A (3, 5) and B (4, 4) lies on the graph of line ax + by = 7. Find the value of a. [Answer: a = – 1]
15. The cost of coloured paper is ₹ 7 more than 1/3 of the cost of white paper. Write this statement in linear equation in two variables. [Answer: 3x – y = 21]
16. Draw the graph of equation x + y = 5.
17. Write the statement in linear equation in two variables showing relationship between Fahrenheit and Celsius. [Answer: F = 9C/5 + 32]
18. If the points A (4, 6) and B (1, 3) lie on the graph of ax + by = 8, then find the value of a and b. [Answer: a = – 4, b = 4]
19. The force exerted to pull a cart is directly proportional to the acceleration produced in the body, write a linear equation in two variables to represent the statement by taking constant mass equal to 3kg. Read form the graph the force (in Newton) required when the acceleration produced is 5m/sec2. [Answer: y = 3x where y = force and x = acceleration. Force = 15 N]
20. Find the value of ‘a’ if (1, -1) is the solution of the equation 2x + ay = 5. Find the other two solutions of the equation. [Answer: a = – 3]
21. Draw the graph of the linear equation 2x + 3y = 6. Find out the coordinates of the points where the two lines intersects at x- axis and y – axis. [Answer: (3, 0) and (0, 2)]
22. Find two solutions of the equation 4x + 5y = 28. Check whether (-2, 10) is the solution of the given equations. [Answer: (2, 4) and (7, 0). (– 2, 10) is not the solution of the given equation]
23. Give the geometrical representation of 5x + 7 = 0 as equation: (i) in one variable (ii) in two variables.
24. The length of the rectangular park is 10 m more than its breadth. Perimeter of the park is 180 m. Find out the dimensions of park using linear equations in two variables. [Answer: 50 m and 40 m]
25. Riya participates in Diwali Mela with her friends for the charity to centre of handicapped children. They donate ₹ 3600 to the centre from the amount earned in Mela. If each girl donates ₹ 150 and each boy donates ₹ 200. (a) Form the linear equation in two variables. (b) If no. of girls are 8, find out no. of boys. (c) What values of Riya & her friends are depicted here? [Answer: (a) 150x + 200y = 3600, (b) Boys = 12, (c) Sincerity, Helpfulness, Cooperation]
26. Draw the graph for the linear equations 3x – 4y = 12. If x = 8 Find the value of y with the help of graph. [Answer: y = 3]
27. Find three different solutions of 3m – 8n = 27. [Answer: (1, – 3), (9, 0) and (– 7, – 6)]
28. Given that F = (9/5) C + 32, now find (i) If the temperature is 350C, what is the temperature in Fahrenheit? (ii) if the temperature is 300C, what is the temperature in Fahrenheit? [Answer: 105 F, 86 F]
29. If x = 3k – 2, y = 2k is a solution of equation 4x – 7y + 12 = 0, then find the value of K. [Answer: K = – 10]
30. Draw the graph of the linear equations 2y – x = 7. With the help of graph check whether x = 3 and y = 2 is the solution of the equation? [Answer: No]
31. Sarika distributes chocolates on the occasion of children’s Day. She gives 5 chocolates to each child and 20 chocolates to adults. If no. of child is represented by ‘x’ and total distributed chocolates as ‘y’. (i) Write it in form of linear equation in two variables. (ii) If she distributed 145 chocolates in total, find out no. of children? (iii) Which values are depicted here? [Answer: (i) 5x – y + 20 = 0, (ii) 25, (iii) Happiness, Sharing and Harmony]
32. Express y in the terms of x: 3y + 5x = 9. [Answer: y = (9 – 5x)/3]
33. Examine whether the point (5, 2) lie on the graph of equation 2x + 3y = 16. [Answer: Yes]
34. Find any two solutions of equation 2x + y = x + 5. [Answer: (1, 4), (0, 5)]
35. Find the value of P if x = 2, y = 3 is a solution of equations: 5x + 3py = 4a. [Answer: P = (4a – 10)/9]
36. A men went to the Bank with ₹ 1000. He asked the cashier to give him ₹ 5 and ₹ 10 notes only in return. Write the linear equation in two variables. If the number of ₹ 10 Notes are 25, then find the number of ₹ 5 Notes? Also represent it graphically? [Answer: 150]
37. Write 3y = 8x in the form of ax + by + c = 0 Write x in terms of y. Find any two solutions of the equation. How many solutions you can find out? [Answer: a = 8, b = – 3, c = 0. Infinite solutions]
38. The age of father is 3 years more than three times the age of his son. There years hence, father’s age will be ten years more than twice the age of the son. Assuming father’s age as x and son’s age as y form two linear equations. [Answer: x – 3y = 3, x – 2y = 13]
39. Rohan and Ramita of Class IX decided to collect ₹ 25 for class cleanliness. Write it in linear equations in two variables. Also draw the graph. What values of both the students are depicted here? [Answer: x + y = 25]
40. Priyanka and Arti decided to donate ₹ 1600 for the earthquake victims in Gujrat considering Priyanka’s share as ‘x’ and Arti share as ‘y’. (a) Form a linear equation in two variables. (b) If Priyanka donates thrice the amount donated by Arti, than find out the amount donated by both. (c) What values of both the children are depicted here? [Answer: (a) 2x + y = 1600, (b) Priyanka ₹ 1200 and Arti ₹ 400, (c) Caring, Sensitivity, Social responsibility and Helpfulness]