Exercise 4.1 appears on page number 68 of the textbook, prescribed according to the NCERT Syllabus. Exercise 4.1, with 2 questions, focuses on the main concepts covered in the 4.2 section of the textbook, which deals with Linear Equations. The subject-matter experts who devised the NCERT solutions have explained them in simple language, thus making it easy for the students to comprehend the concepts.
The NCERT Solutions for Class 9 Maths are helpful for students who wish to ace the board exams. Meanwhile, this chapter comes under the unit Geometry. The final paper usually has about 7 questions from the unit Geometry, thus constituting 20 marks weightage in the question paper. At the same time, the NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1 is also prepared after thorough research and in strict adherence to the NCERT syllabus guidelines.
NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables Exercise 4.1
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NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables Exercise 4.1
1. 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)
Solution:
Let the cost of a notebook be ₹ x
Let the cost of a pen be ₹ y
According to the question,
The cost of a notebook is twice the cost of a pen.
So, cost of a notebook = 2×Cost of a pen
x = 2×y
x = 2y
x-2y = 0
x-2y = 0 is the linear equation in two variables representing the statement ‘The cost of a notebook is twice the cost of a pen’.
2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(ii) x –(y/5)–10 = 0
Solution:
The equation x –(y/5)-10 = 0 can be written as,
1x+(-1/5)y +(–10) = 0
Now comparing x+(-1/5)y+(–10) = 0 with ax+by+c = 0
We get,
a = 1
b = -(1/5)
c = -10
(iii) –2x+3y = 6
Solution:
–2x+3y = 6
Re-arranging the equation, we get,
–2x+3y–6 = 0
The equation –2x+3y–6 = 0 can be written as,
(–2)x+3y+(– 6) = 0
Now comparing (–2)x+3y+(–6) = 0 with ax+by+c = 0
We get, a = –2
b = 3
c =-6
(iv) x = 3y
Solution:
x = 3y
Re-arranging the equation, we get,
x-3y = 0
The equation x-3y=0 can be written as,
1x+(-3)y+(0)c = 0
Now comparing 1x+(-3)y+(0)c = 0 with ax+by+c = 0
We get, a = 1
b = -3
c =0
(v) 2x = –5y
Solution:
2x = –5y
Re-arranging the equation, we get,
2x+5y = 0
The equation 2x+5y = 0 can be written as,
2x+5y+0 = 0
Now comparing 2x+5y+0= 0 with ax+by+c = 0
We get, a = 2
b = 5
c = 0
(vi) 3x+2 = 0
Solution:
3x+2 = 0
The equation 3x+2 = 0 can be written as,
3x+0y+2 = 0
Now comparing 3x+0+2= 0 with ax+by+c = 0
We get, a = 3
b = 0
c = 2
(vii) y–2 = 0
Solution:
y–2 = 0
The equation y–2 = 0 can be written as,
0x+1y+(–2) = 0
Now comparing 0x+1y+(–2) = 0with ax+by+c = 0
We get, a = 0
b = 1
c = –2
(viii) 5 = 2x
Solution:
5 = 2x
Re-arranging the equation, we get,
2x = 5
i.e., 2x–5 = 0
The equation 2x–5 = 0 can be written as,
2x+0y–5 = 0
Now comparing 2x+0y–5 = 0 with ax+by+c = 0
We get, a = 2
b = 0
c = -5
Exercise 4.1 from the NCERT Solutions of Class 9 Maths Chapter 4- Linear Equations has 2 questions. Question 1 from this exercise asks students to write a linear equation in two variables to represent the statement that the cost of a notebook is twice that of a pen. Students can also learn more about the concept with the help of Question 2 under this exercise.
As per the syllabus, Unit 2 of Class 9 Mathematics Geometry has two chapters, one of which is Linear Equation in Two Variables, and about 20 marks out of the total 80 for Class 9 Maths are assigned to this unit. Here is the format of the 2 questions that are asked in Exercise 4.1, that is, the first exercise of Chapter 4. Question number 1 in this is a short answer question, and Question number 2, from Exercise 4.1, contains a main question, which requires you to solve about 8 equations, which are asked as sub-questions under it.
Solving this Exercise from Chapter 4 of NCERT Solutions for Class 9 Maths can help you to clear your doubts and learn more in-depth concepts about the topic more effectively. You can also see other benefits here:
- Get a clear idea about the formula and the concepts explained in the exercise
- Learn the chapter more thoroughly
- Get acquainted with the various types of questions asked
- Improve speed and accuracy by getting more practice solving questions
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