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.
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
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.
Q2 Write four solutions for each of the following equations:
(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 .
Q3 (i) Check which of the following are solutions of the equation and which are not: ((0,2)
(i) Given :
Putting ,
we have ,
Therefore, is not a solution of .
Q3 (ii) Check which of the following are solutions of the equation and which are not: (2,0)
Given :
Putting (2,0),
we have ,
Therefore, (2,0) is not a solution of .
Q3 (iii) Check which of the following are solutions of the equation and which are not: (4,0)
Given :
Putting (4,0),
we have ,
Therefore, (4,0) is a solution of .
Q3 (iv) Check which of the following are solutions of the equation and which are not:
Given :
Putting ,
we have ,
Therefore, is not a solution of .
Q3 (v) Check which of the following are solutions of the equation and which are not: (1,1)
Given :
Putting (1,1) ,
we have ,
Therefore, (1,1) is not a solution of .
Q4 Find the value of k, if , is a solution of the equation .
Given :
Putting (2,1),
we have ,
Therefore, k=7 for putting x=2 and y=1.
Given :
Putting x=0,we have
Putting x=1,we have
Thus, (0,4) and (1,3) are solutions of given equation.
Q1 (ii) 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, (0,2) and (1,1) are solutions of given equation.
Q1 (iii) 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, (0,0) and (1,3) are solutions of given equation.
Q1 (iv) 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, (0,3) 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.
Q3 If the point (3, 4) lies on the graph of the equation , find the value of a.
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 :
Q5 (A) From the choices given below, choose the equation whose graph is given in Fig. 4.6.
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.
Q5 (B) From the choices given below, choose the equation whose graph is given in Fig. 4.7
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 the 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 xaxis and Fahrenheit for the yaxis.
Let celsius be on xaxis and Fahrenheit be on yaxis.
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,
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 .
Let temperature be x in both Fahrenheit and celsius.
Thus, 40 is the temperature which is numerically the same in both Fahrenheit and celsius.
Q1 (i) Give the geometric representations of as an equation
in one variable
Equation can be represented in one variable on number line.
Q1 (ii) Give the geometric representations of as an equation: in two variables
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.
Q2 (i) Give the geometric representations of as an equation: in one variable
Equation can be represented in one variable on the number line.
The yellow mark represents x=  4.5.
Q2 (ii) Give the geometric representations of as an equation: in two variables
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.
Chapter No. 
Chapter Name 
Chapter 1 

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 

Chapter 7 

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 

Chapter 11 
CBSE NCERT solutions for class 9 maths chapter 11 Constructions 
Chapter 12 

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 
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!
2.(ii) Give the geometric representations of as an equation
(ii) in two variables
2. Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?
1.(iv) Draw the graph of each of the following linear equations in two variables:
(iv)