Chapter 4 : Linear Equations in Two Variables  Ncert Solutions for Class 9 Maths CBSE
If you love numbers & have a deep interest in statistics, then Mathematics is probably one of the scoring subject ever. A Class 9th CBSE Mathematics is one of the challenging subject one can undergo as, it involves a lot of crunching of complex numbers, geometrical formulae, diagrams & much more. Hence, to simplify the mathematical complexity, TopperLearning has framed a customise solution that involves Test preparation notes, Textbook solutions, Videos, & several other study material that help the student to memorise the concepts quickly. We have bifurcated our CBSE Class 9 Study Material (Solution) into 3 Different parts namely:
 CBSE Class 9 Practice Test includes Revision notes, Question bank & Sample Paper
 TopperLearning Classroom that includes Videos, Ask the Experts & Preparation Tips
 Text Book Solutions, etc
TopperLearning packages involves all the ingredients of CBSE Class 9 Study Material that includes Solved Question Papers, High Animated Videos, Solutions by SME (Subject Matter Expert), CBSE class 9 Preparation Tips, Update to CBSE 9th Mathematics syllabus, Practice books, Reference Materials, etc that help you to score great marks with glorious marks.
Getting a good score is now relatively easy if you prefer TopperLearning solutions for CBSE Class 9th Mathematics subject. By purchasing our package, you will be accessed to guaranteed success in your examination!
Chapter 4  Linear Equations in Two Variables Excercise Ex. 4.1
x = 2y
x  2 y = 0
 2x + 3 y  6 = 0
a =  2, b = 3, c =  6
1x  3y + 0 = 0
Comparing this equation with ax + by + c = 0
a = 1, b =  3, c = 0
2x + 5y + 0 = 0
a = 2, b = 5, c = 0
3x + 0.y + 2 = 0
a = 3, b = 0, c = 2
0.x + 1.y  2 = 0
a = 0, b = 1, c =  2
 2x + 0.y + 5 = 0
Company this equation with ax + by + c = 0
a =  2, b = 0, c = 5
Chapter 4  Linear Equations in Two Variables Excercise Ex. 4.2
Hence, the correct answer is (iii).
For x = 0
2(0) + y = 7
For x = 1
2(1) + y = 7
2(2) + y = 7
y = 3
For x = 1
(1) + y =9
For x = 0
0 = 4y
For y = 1
x = 4(1) = 4
So, (4, 1) is a solution of this equation
For y =  1
x = 4(1)
x = 4
So, (4,  1) is a solution of this equation
For x = 2
2 = 4y
Putting x = 0, and y = 2 in the L.H.S of given equation
x  2y = 0  (22 )
L.H.S # R.H.S
So (0, 2) is not a solution of this equation.
x  2y = 2  (2 0)
L.H.S R.H.S
So (2, 0) is not a solution of this equation.
Putting x = 4, and y = 0 in the L.H.S of given equation
x  2y = 4  2(0)
= 4 = R.H.S
So (4, 0) is a solution of this equation.
L.H.S R.H.S
So is not a solution of this equation.
Putting x = 1, and y = 1 in the L.H.S of given equation
x  2y = 1  2(1)
L.H.S R.H.S
So (1, 1) is not a solution of this equation.
2(2) + 3(1) = k
4 + 3 = k
k = 7
Chapter 4  Linear Equations in Two Variables Excercise Ex. 4.3
x 
0 
4 
y 
4 
0 
x 
4 
2 
y 
2 
0 
Now we can draw the graph of above equation as following
We may observe that x =  1, y =  3 and x = 1, y = 3 are solutions of above equation. So our solution table is
x 
 1 
1 
y 
 3 
3 
Now we may draw the graph of above equation as following
x 
0 
1 
y 
3 
1 
Now we may construct the graph of this equation as below
2x + y 18 = 0.
As we know that through one point, infinite number of lines can pass through.
So, there are infinite lines of such type passing through given point.
3y = ax + 7
3 (4) = a (3) + 7
5 = 3a
a =
Fair for 1st kilometre = Rs .8
Fair for rest distance = (x  1) 5
Total fair = 8 + (x  1) 5
y = 8 + 5x  5
y = 5x + 3
5x  y + 3 = 0
x 
0 

y 
3 
0 
We may observe that coordinates of the points of the graph satisfy the equation x + y = 0.
So, x + y = 0 is the equation corresponding to graph as shown in the first figure.
Hence (ii) is the correct answer.
So y =  x + 2 is the equation corresponding to the graph shown in the second figure.
Hence,
Work done distance traveled
w d
w = kd
Where k is a constant
If constant force is 5 units, work done w = 5d
Now we may observe that point (1, 5) and (1, 5) satisfy the above equation.
So (1, 5) and (1, 5) are solutions of this equation.
The graph can be drawn as follows:
(ii) From the graphs we may observe that the value of y corresponding to x = 0 is 0. Thus the work done by the body is 0 units when the distance traveled by it is 0 unit.
Amount contributed by Yamini + amount contributed by Fatima = 100
x + y = 100
Now we observe that (100, 0) and (0, 100) satisfy the above equation.
So, (100, 0) and (0, 100) are solutions of above equation.
The graph of equation x + y = 100 can be drawn as follows:
Now we can draw the graph of above equation as below
If F = 0^{o}
Chapter 4  Linear Equations in Two Variables Excercise Ex. 4.4
In two variables y = 3 represents a straight line passing through point (0, 3) and parallel to x axis. As it is a collection of all points of plane which are having their y coordinate as 3
(2) In two variables 2x + 9 = 0 represents a straight line passing through point ( 4.5, 0) and parallel to y axis. As it is a collection of all points of plane, having their x coordinate as 4.5.
CBSE Class 9 Maths Homework Help
Clear all your doubts instantly at our “Ask Doubt” section. Get expert help and guidance at your comfort. To know the syllabus in detail, click here.
NCERT Textbooks are the rich stimulant for those students who want to score better in the CBSE examinations. By solving our papers the students have achieved a better and higher result. One of the primary objectives of creating ncert solution for class 9 is that the student gets access to an easy solution; which acts as a strong catalyst in improving the marks. We usually focus that the students don’t find any difficulty in understanding the concepts and can memorize them easily.
Kindly Sign up for a personalised experience
 Ask Study Doubts
 Sample Papers
 Past Year Papers
 Textbook Solutions
Sign Up
Verify mobile number
Enter the OTP sent to your number
Change