# NCERT Solutions for Class 9 Maths Chapter 4

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1, Exercise 4.2, Exercise 4.3 and Exercise 4.4 Linear Equations in Two Variables for CBSE first term exams free PDF to downloads updated for academic session 2021-2022 following new NCERT Books. UP Board Solutions for Class 9 Maths Chapter 4 Prashnavali 4.1, Prashnavali 4.2, Prashnavali 4.3 and Prashnavali 4.4 are given below in Hindi Medium. View UP Board Solution and NCERT Solutions for 2021-22 in Video Format Hindi Medium and English Medium or free download in PDF or use it as online all the digital contents. There is not any login or registration condition.

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## NCERT Solutions for Class 9 Maths Chapter 4

### 9th Maths Chapter 4 Solutions in English & Hindi Medium

 Class: 9 Maths (English and Hindi Medium) Chapter 4: Linear Equations in Two Variables

NCERT Solutions for Class 9 Maths Chapter 4 all exercises are given below. NCERT Solutions 2021-22 are updated for the CBSE Exams 2021 based on Latest CBSE Syllabus 2021-2022. NCERT Solutions and UP Board Solutions for Class 9 Maths Chapter 4 as online contents are helpful for all the CBSE, MP Board, Gujrat Board & UP Board (High School) students who are following NCERT Books for their Examination.

#### Class 9 Maths Chapter 4 Exercise 4.1 Solution in Video

Class 9 Maths Chapter 4 Exercise 4.1 Solution
Class 9 Maths Exercise 4.1 Question wise Solution

#### Class 9 Maths Chapter 4 Exercise 4.2 Solution in Video

Class 9 Maths Exercise 4.2 Question 1, 2 Solution
Class 9 Maths Exercise 4.2 Question 3, 4 Solution

Class 9 Maths Chapter 4 Exercise 4.2 Solution
Class 9 Maths Chapter 4 Exercise 4.3 Solution

#### Class 9 Maths Chapter 4 Exercise 4.3 Solution in Video

Class 9 Maths Exercise 4.3 Question 1, 2 Solution
Class 9 Maths Exercise 4.3 Question 3, 4 Solution

Class 9 Maths Exercise 4.3 Question 5, 6 Solution
Class 9 Maths Exercise 4.3 Question 7 Solution

#### Class 9 Maths Chapter 4 Exercise 4.4 Solution in Video

Class 9 Maths 4 Exercise 4.4 Question wise Solution
Class 9 Maths Chapter 4 Exercise 4.4 Solution

### Class 9 Maths Chapter 4 Practice Questions with Solutions

##### When is the solution of a linear equation is not affected?

The solution of a linear equation is not affected when
1.The same number is added to (or subtracted from) both sides of the equation.
2. Both sides of the equation are multiplied (or divided) by the same non-zero number.

##### What is meant by a solution of the linear equation?

The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.

#### Important Notes on 9th Maths Chapter 4

• An algebraic equation is a statement of equality of algebraic expression involving one or more variables.
• An equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers (a and b together cannot be zero) and x, y are variables, is called a liner equation in two variables.
• A linear equation in one variable (say x) can be written as linear equation in two variables, by taking coefficient of other variable (say y) as zero.
##### Important Point in 9th Maths Chapter 4
1. Every solution of the linear equation cab be represented by a unique point on the graph of the equation.
x = 0 is the equation of the Y- axis and y = 0 is the equation of the X-axis.
2. The graph of x = a represents a straight line parallel to the Y-axis and the graph of y = a represent a straight line parallel to the X-axis.
3. An equation of the type y = mx represents a straight line through the origin.

### Important Questions on 9th Maths Chapter 4

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

Equation of two lines passing through (2,14) are given by: x+y=16 and 8x-y = 2. There are infinite number of lines that can pass through (2, 4) as infinite number of lines passes through a point.

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

Given equation of line: 3y = ax + 7. Putting x = 3 and y = 4, we have, 3 × 4 = a × 3 + 7 ⇒ 12 = 3a + 7 ⇒ 12 – 7 = 3a ⇒ a = 5/3

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

Given that: Distance traveled = x km and total fare = ₹ y Total fare = Fare for first km + Fare for remaining distance Therefore, the equation: y = 8 + 5×(x – 1) ⇒ y = 5x + 3

##### 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 ₹ x and that of a pen to be ₹ y).

Here, the cost of notebook = ₹ x and the cost of pen =₹ y According to question, Cost of notebook = 2 × Cost of Pen ⇒ x = 2y ⇒ x – 2y = 0

##### Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c: 2x + 3y = 9.35.

2x + 3y = 9.35 ⇒ 2x + 3y – 9.35 = 0 Hence, Here a = 2, b = 3 and c = – 9.35.

##### What are the main objectives of chapter 4 class 9th Maths?

The main objectives of chapter 4 Linear Equations in Two Variables of class 9th Maths are to teach students:

1. The meaning of Linear Equations in Two Variables.
2. How to find solutions of Linear Equations in Two Variables.
3. How to draw the graph of Linear Equations in Two Variables.
4. About equations of lines parallel to the x-axis and y-axis.
##### What are the main points of chapter 4 of class 9th Maths to remember for first term exam?

The main points of chapter 4 of class 9th Maths that students must remember at the time of exam are:

1. An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
2. A linear equation in two variables has infinitely many solutions.
3. The graph of every linear equation in two variables is a straight line.
4. x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
5. The graph of x = a is a straight line parallel to the y-axis.
6. The graph of y = a is a straight line parallel to the x-axis.
7. An equation of the type y = mx represents a line passing through the origin.
8. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Moreover, every solution of the linear equation is a point on the graph of the linear equation.
9. An easy way of getting a solution is to take x = 0 and get the corresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.
##### Which exercise of chapter 4 of class 9th Maths has the highest number of sums?

In chapter 4 of class 9th Maths, there are four exercises.
The first exercise (Ex 4.1) contains two questions and two examples (examples 1, 2).
The second exercise (Ex 4.2) contains four questions and two examples (examples 3, 4).
The third exercise (Ex 4.3) contains eight questions and four examples (examples 5, 6, 7, 8).
The fourth (last) exercise (Ex 4.4) contains two questions and one example (example 9).
So, the third exercise (Ex 4.3) has the highest number of sums.

##### How can students get good marks in chapter 4, Linear Equations in Two Variables of 9th Maths?

Chapter 4 of class 9th Maths contains nine examples and 16 questions. All questions and examples of this exercise are nice and interesting. So, to get good marks in chapter 4 of class 9th Maths, students should practice all questions and examples of this chapter.                