#### Chapters

Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equations in two Variables

Chapter 5: Introduction to Euclid's Geometry

Chapter 6: Lines and Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Areas of Parallelograms and Triangles

Chapter 10: Circles

Chapter 11: Constructions

Chapter 12: Heron's Formula

Chapter 13: Surface Area and Volumes

Chapter 14: Statistics

Chapter 15: Probability

#### NCERT Mathematics Class 9

## Chapter 4: Linear Equations in two Variables

#### Chapter 4: Linear Equations in two Variables Exercise 4.10 solutions [Page 68]

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be Rs. x and that of a pen to be Rs. y).

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- `2x+3y=9.3bar5`

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- `x-y/5-10=0`

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- –2x + 3y = 6

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- x = 3y

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

2x = –5y

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

3x + 2 = 0

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

y – 2 = 0

5 = 2x

#### Chapter 4: Linear Equations in two Variables Exercise 4.20 solutions [Page 70]

Which one of the following options is true, and why?

y = 3x + 5 has

(i) a unique solution, (ii) only two solutions, (iii) infinitely many solutions

Write four solutions for the following equation:- 2x + y = 7

Write four solutions for the following equation:- πx + y = 9

Write four solutions for the following equation:- x = 4y

Check if (0, 2) is the solution of the equation x - 2y = 4.

Check if (2, 0) is the solution of the equation x - 2y = 4.

Check if (4, 0) is the solution of the equation x - 2y = 4.

Check if `(sqrt2", "4sqrt2)` is the solution of the equation x - 2y = 4.

Check if (1, 1) is the solution of the equation x - 2y = 4.

Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

#### Chapter 4: Linear Equations in two Variables Exercise 4.30 solutions [Page 74]

Draw the graph of the following linear equations in two variables:- x + y = 4

Draw the graph of the following linear equations in two variables:- x – y = 2

Draw the graph of the following linear equations in two variables:- y = 3x

Draw the graph of the following linear equations in two variables:- 3 = 2x + y

Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

The taxi fare in a city is as follows:- For the first kilometre, the fare is Rs. 8 and for the subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

From the choices given below, choose the equation whose graphs are given in the given figures.

**For the first figure**

(i) y = *x*

(ii) x* *+ *y* = 0

(iii) y* *= 2*x*

(iv) 2* + 3y = 7x*

**For the second figure**

(i) *y* = *x* +2

(ii) *y* = *x* − 2

(iii) *y* = − *x* + 2

(iv) *x* + 2*y* = 6

If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is

(i) 2 units (ii) 0 unit

Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs. x and Rs. y.) Draw the graph of the same.

In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:-

`F=(9/5)C+32`

(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.

(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?

(iii) If the temperature is 95°F, what is the temperature in Celsius?

(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?

(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

#### Chapter 4: Linear Equations in two Variables Exercise 4.40 solutions [Page 77]

Give the geometric representations of y = 3 as an equation in one variable.

Give the geometric representations of y = 3 as an equation in two variables.

Give the geometric representations of 2x + 9 = 0 as an equation in one variable.

Give the geometric representations of 2x + 9 = 0 as an equation in two variables.

## Chapter 4: Linear Equations in two Variables

#### NCERT Mathematics Class 9

#### Textbook solutions for Class 9

## NCERT solutions for Class 9 Mathematics chapter 4 - Linear Equations in two Variables

NCERT solutions for Class 9 Maths chapter 4 (Linear Equations in two Variables) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Class 9 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Mathematics chapter 4 Linear Equations in two Variables are Introduction of Linear Equations, Solution of a Linear Equation, Graph of a Linear Equation in Two Variables, Concept of Linear Equations in Two Variables, Equations of Lines Parallel to the X-axis and Y-axis.

Using NCERT Class 9 solutions Linear Equations in two Variables exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer NCERT Textbook Solutions to score more in exam.

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