# NCERT Solutions for class 9 Maths Chapter 4- Linear Equations In Two Variables Exercise 4.1

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, where it deals with Linear Equations. The subject matter experts who devised the solutions have explained it in simple language, thus making it easy for the students to comprehend the concept.

The NCERT Solutions for Class 9 Maths are helpful for students who wish to ace the first and second term 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- Linear Equations In Two Variables Exercise 4.1 is also prepared after thorough research and in strict adherence to the NCERT syllabus guidelines.

### Access other exercise solutions of class 9 Maths Chapter 4-Linear Equations In Two Variables

Exercise 4.2 Solutions

Exercise 4.3 Solutions

Exercise 4.4 Solutions

## 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 â‚¹ x and that of a pen to be â‚¹ y)

Solution:

Let the cost of a notebook to be = â‚¹ x

Let the cost of a pen to be = â‚¹ y

According to the question,

The cost of a notebook is twice the cost of a pen.

i.e., Cost of a notebook = 2Ã—Cost of a pen

x = 2Ã—y

x = 2y

x-2y = 0

x-2y = 0 is the linear equation in two variables to represent the statement â€˜The cost of a notebook is twice the cost of a penâ€™.

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 â€“(y/5)â€“10 = 0

Solution:

The equation x â€“(y/5)-10 = 0 can be written as,

1x+(-1/5)y +(â€“10) = 0

Now comparing x+(-1/5)y+(â€“10) = 0 with ax+by+c = 0

We get,

a = 1

b = -(1/5)

c = -10

(iii) â€“2x+3y = 6

Solution:

â€“2x+3y = 6

Re-arranging the equation, we get,

â€“2x+3yâ€“6 = 0

The equation â€“2x+3yâ€“6 = 0 can be written as,

(â€“2)x+3y+(â€“ 6) = 0

Now comparing (â€“2)x+3y+(â€“6) = 0 with ax+by+c = 0

We get, a = â€“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 = â€“5y

Solution:

2x = â€“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) yâ€“2 = 0

Solution:

yâ€“2 = 0

The equation yâ€“2 = 0 can be written as,

0x+1y+(â€“2) = 0

Now comparing 0x+1y+(â€“2) = 0with ax+by+c = 0

We get, a = 0

b = 1

c = â€“2

(viii) 5 = 2x

Solution:

5 = 2x

Re-arranging the equation, we get,

2x = 5

i.e., 2xâ€“5 = 0

The equation 2xâ€“5 = 0 can be written as,

2x+0yâ€“5 = 0

Now comparing 2x+0yâ€“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 one 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 is assigned to this unit. Here, the format of the 2 questions that are asked in the 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 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 from 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 the speed and accuracy by getting more practice solving questions