# NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables- In previous classes, you have studied linear equations in one variable. In this particular chapter, you will study linear equations in two variables of the type ax+by+c=0 where a, b and c are the real numbers, and a and b both are not zero. Solutions of NCERT for class 9 maths chapter 4 Linear Equations in Two Variables are there to make your task easy while preparing for the exams. In this chapter, there are a total of 4 exercises which consist of 16 questions. CBSE NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables is covering the detailed solutions to each and every questions present in the practice exercises. This is an important chapter as this created a foundation for the higher level of algebra. Algebra is a unit in class 9 maths which holds 20 marks in the final examination. This chapter always comes with a good number of questions in competitive exams like the Indian National Olympiad (INO), National Talent Search Examination (NTSE). NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables are designed in such a manner that a student can get maximum marks assigned to that particular question. NCERT solutions are also available classwise and subject wise which can be downloaded by clicking on the given link.

### Q1 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).

Let the cost of a notebook be Rs x and that of a pen be Rs y.

According to the given condition: The cost of a notebook is twice the cost of a pen.

Thus,

Given :

Here , a=2, b=3  and c =

Given:

Here ,

a=1,

c = -10

Given :

Here , a= -2, b=3  and c = -6

Given :

Here , a= 1, b= -3  and c =0

Given :

Here , a=2, b= 5  and c =0

Given :

Here , a= 3, b=0  and c =2

Given :

Here , a=0, b= 1  and c = -2

Given :

Here , a=2, b= 0 and c = -5

## NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.2

### (iii) infinitely many solutions

Given :

This equation is of a line and a line has infinite points on it and each point is a solution Thus, (iii) infinitely many solutions is the correct option.

(i)                 (ii)                 (iii)

(i) Given :

Putting x=0, we have ,  means   is a solution.

Putting x=1, we have ,  means   is a solution.

Putting x=2, we have ,  means   is a solution.

Putting x=3, we have ,  means   is a solution.

The four solutions are :.

(ii) Given :

Putting x=0, we have ,  means   is a solution.

Putting x=1, we have ,  means   is a solution.

Putting x=2, we have ,  means  is a solution.

Putting x=3, we have ,  means  is a solution.

The four solutions are :.

(iii) Given :

Putting x=0, we have ,  means   is a solution.

Putting x=1, we have ,  means   is a solution.

Putting x=2, we have ,  means   is a solution.

Putting x=3, we have ,  means   is a solution.

The four solutions are :,, and .

(i) Given :

Putting ,

we have ,

Therefore, is not a solution of .

Given :

Putting  (2,0),

we have ,

Therefore, (2,0) is not a solution of .

Given :

Putting  (4,0),

we have ,

Therefore, (4,0) is a solution of .

Given :

Putting  ,

we have ,

Therefore,  is not a solution of .

Given :

Putting  (1,1) ,

we have ,

Therefore,   (1,1)  is not a solution of .

Given :

Putting  (2,1),

we have ,

Therefore, k=7 for  putting x=2 and y=1.

## NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.3

### Q1 (i) Draw the graph of each of the following linear equations in two variables:

Given : Putting x=0,we have

Putting x=1,we have

Thus, (0,4) and (1,3) are solutions of given equation.

Given : Putting x=0,we have

Putting x=1,we have

Thus, (0,-2) and (1,-1) are solutions of given equation.

Given : Putting x=0,we have

Putting x=1,we have

Thus, (0,0) and (1,3) are solutions of given equation.

Given : Putting x=0,we have

Putting x=1,we have

Thus, (0,3) and (1,1) are solutions of given equation.

The equations of two lines passing through (2, 14) are given by :

There are infinite lines passing through (2, 14) because infinite lines pass through a point.

Given : the point (3, 4) lies on the graph of the equation

Put x=3 and y=4

Given: The distance covered as x km and total fare is Rs. y.

Total fare =the fare for first km + the fare of the remaining  distance

For graph,

Putting x=0, we have

Putting x=1, we have

Putting x=2, we have

Hence,(0,3),(1,8) and (2,13)  are solutions of equation.

The graph is as shown : (i)

(ii)

(iii)

(iv) For the given figure :

Points on line are (-1,1) ,  (0,0 ) and (1,-1)

satisfies all the above points.

Thus,  is the correct equation of the line.

(i)

(ii)

(iii)

(iv) For the given figure :

Points on line are (-1,3) ,  (0,2 ) and (2,0)

satisfies all the above points.

Thus,  is the correct equation of the line.

Let work done be y and distance be x.

Given : Constant force = 5 units

Work done by a body on application of a constant force is directly proportional to the distance travelled by the body.

i.e.

k=Constant force = 5

Then,

For graph,

Put x=0,we have

Put x=1,we have

Put x=2,we have

Points are (0,0)   ,  (0,5)   and  (2,10)

If diatance travelled is 2 units than work done is 10  units. Let work done be y and distance be x.

Given : Constant force = 5 units

Work done by a body on application of a constant force is directly proportional to the distance travelled by the body.

i.e.

k=Constant force = 5

Then,

For graph,

Put x=0,we have

Put x=1,we have

Put x=2,we have

Points are (0,0)   ,  (0,5)   and  (2,10)

If diatance travelled is 0 units than work done is 0  units. Let contribution of yamini be x.

contribution of yamini be y.

According to question,

For x=0 , we have

For x=10 , we have

For x=20 , we have

Hence, (0,100) , (10,90)  and  (20,80) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis.

Let celsius be on x-axis and Fahrenheit be on y-axis.

For graph,

Putting  x=0, we get

Putting  x=5, we get

Putting  x=10, we get

Hence, points are  (0,32) , (5,41)   and (10,50). If the temperature is 30°C, what is the temperature in Fahrenheit?

Put c=30,

Thus, the temperature = 30°C, then the temperature is 86 in Fahrenheit.

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

Put F=95,

If the temperature is 95°F, then 35 is the temperature in Celsius.

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?

If the temperature is 0°C,

if the temperature is 0°F,

Thus, if the temperature is 0°C ,then temperature in fahrenheit is 32 and  if the temperature is 0°F ,then temperature in celsius is -17.8 .

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

Let temperature be x in both Fahrenheit and celsius.

Thus, 40 is the temperature which is numerically the same in both Fahrenheit and celsius.

## NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables Excercise: 4.4

in one variable

Equation  can be represented in one variable on number line. For 2 variable representation of .

Equation :

For graph,

x=0,we have y=3

x=1,we have y=3

x=2,we have y=3

Hence, (0,3) ,(1,3) and (2,3)  are solutions of equation. Equation  can be represented in one variable on the number line.

The yellow mark represents x=  - 4.5. For 2 variable representation of .

Equation :

For graph,

y=0,we have

y=1,we have

y=2,we have

Hence,  ,   and      are solutions of equation. ## NCERT solutions for class 9 maths chapter wise

 Chapter No. Chapter Name Chapter 1 NCERT solutions for class 9 maths chapter 1 Number Systems Chapter 2 CBSE NCERT solutions for class 9 maths chapter 2 Polynomials Chapter 3 Solutions of NCERT class 9 maths chapter 3 Coordinate Geometry Chapter 4 NCERT solutions for class 9 maths chapter 4 Linear Equations In Two Variables Chapter 5 CBSE NCERT solutions for class 9 maths chapter 5 Introduction to Euclid's Geometry Chapter 6 Solutions of NCERT class 9 maths chapter 6 Lines And Angles Chapter 7 NCERT solutions for class 9 maths chapter 7 Triangles Chapter 8 CBSE NCERT solutions for class 9 maths chapter 8 Quadrilaterals Chapter 9 Solutions of NCERT class 9 maths chapter 9 Areas of Parallelograms and Triangles Chapter 10 NCERT solutions for class 9 maths chapter 10 Circles Chapter 11 CBSE NCERT solutions for class 9 maths chapter 11 Constructions Chapter 12 Solutions of NCERT class 9 maths chapter 12 Heron’s Formula Chapter 13 NCERT solutions for class 9 maths chapter 13 Surface Area and Volumes Chapter 14 CBSE NCERT solutions for class 9 maths chapter 14 Statistics Chapter 15 Solutions of NCERT class 9 maths chapter 15 Probability

## How to use NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables

• First of all, go through the conceptual text given in the NCERT textbook.

• Then understand the application of concepts in the examples.

• After this, you should come over practice exercises.

• While practicing the exercises, you can use NCERT solutions for class 9 maths chapter 4 Linear Equations in Two Variables as a reference.

• After the completion of all the above points, you can practice the questions of past year papers.

Keep Working Hard & Happy Learning!