# NCERT Solutions for Class 9 Maths Chapter 4

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1, Exercise 4.2, Exercise 4.3 and Exercise 4.4 Linear Equations in Two Variables View in Video Format in Hindi Medium and English Medium free download in PDF or use it as online digital contents. Download Class 9 Maths App for Offline use or Download कक्षा 9 गणित App for offline use.

 Class 9: Maths – गणित Chapter 4: Linear Equations in two Variables ## NCERT Solutions for Class 9 Maths Chapter 4

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

These NCERT Solutions are updated for the CBSE Exams 2020 based on Latest CBSE Syllabus 2019-2020. These online contents are helpful for all the CBSE, MP Board, Gujrat Board & UP Board (High School) students who are following NCERT Books for their Examination.

### 9 Maths Exercise 4.1 Solutions in English

NCERT Solutions for class 9 Maths chapter 4 Exercise 4.1 Linear equations in two variables English Medium free to use online or download. Move to Exercise 4.2 or Exercise 4.3 or Exercise 4.4 or Hindi Medium or View in Video Format Solutions. Download Class 9 Maths App for Offline use. #### 9 Maths Exercise 4.2 Solutions in English

9 Maths Chapter 4 Exercise 4.2 in English medium for all the students of CBSE, MP Board, Gujrat Board and UP Board High School who are following NCERT Books. Move to Exercise 4.1 or Exercise 4.3 or Exercise 4.4 or Hindi Medium or View in Video Format Solutions. Download Class 9 Maths App for Offline use.  ##### 9 Maths Exercise 4.3 Solutions in English

Exercise 4.3 of class 9 Maths solutions in English free for all users download or go for online study. All board using NCERT books. Move to Exercise 4.1 or Exercise 4.2 or Exercise 4.4 or Hindi Medium or View in Video Format Solutions. Download Class 9 Maths App for Offline use.    ###### 9 Maths Exercise 4.4 Solutions in English

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.4 in English medium for download and for Study online. This exercise is based on plotting the linear equations in one and two variables. Move to Exercise 4.1 or Exercise 4.2 or Exercise 4.3 or Hindi Medium or View in Video Format Solutions.. Download Class 9 Maths App for Offline use. ### 9 Maths Exercise 4.1 Solutions in Hindi

NCERT Solutions for class 9 Maths chapter 4 Exercise 4.1 Linear equations in two variables in Hindi Medium free to use online or offline. Click here to see प्रश्नावली4.2 or प्रश्नावली 4.3 or प्रश्नावली 4.4 or English Medium or View in Video Format Solutions. Download कक्षा 9 गणित App for offline use. #### 9 Maths Exercise 4.2 Solutions in Hindi

9 Maths Chapter 4 Exercise 4.2 in Hindi Medium for CBSE and UP Board in new academic year 2019-20 using NCERT Textbooks. Click here to see प्रश्नावली4.1 or प्रश्नावली 4.3 or प्रश्नावली 4.4 or English Medium or View in Video Format Solutions. Download कक्षा 9 गणित App for offline use.  ##### 9 Maths Exercise 4.3 Solutions in Hindi

Solutions of Exercise 4.3 of Class 9 Maths in Hindi medium is available free to use or download in PDF. Free for all users without any Login or Password. Click here to see प्रश्नावली4.1 or प्रश्नावली 4.2 or प्रश्नावली 4.4 or English Medium or View in Video Format Solutions. Download कक्षा 9 गणित App for offline use.    ###### 9 Maths Exercise 4.4 Solutions in Hindi

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.4 in Hindi medium for all user whether they are from CBSE board or from UP Board High School. Click here to see प्रश्नावली4.1 or प्रश्नावली 4.2 or प्रश्नावली 4.3 or English Medium or View in Video Format Solutions. Download कक्षा 9 गणित App for offline use. ### 9 Maths Chapter 4 Exercise 4.1, 4.2, 4.3 & 4.4 Sols in Video

NCERT Solutions for class 9 Maths Exercise 4.1 in video format with complete description.

NCERT Solutions for class 9 Maths Exercise 4.2 in video format with complete description.

NCERT Solutions for class 9 Maths Exercise 4.3 in video format with complete description.

NCERT Solutions for class 9 Maths Exercise 4.4 in video format with complete description.

##### Important Terms on Linear Equations
• An algebraic equation is a statement of equality of algebraic expression involving one or more variables.
• An equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers (a and b together cannot be zero) and x, y are variables, is called a liner equation in two variables.
• A linear equation in one variable (say x) can be written as linear equation in two variables, by taking coefficient of other variable (say y) as zero.
• The solution of a linear equation is not affected when
1. The same number is added to (or subtracted from) both sides of the equation.
2. Both sides of the equation are multiplied (or divided) by the same non-zero number.
• The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.
• Every solution of the linear equation cab be represented by a unique point on the graph of the equation.
x = 0 is the equation of the Y- axis and y = 0 is the equation of the X-axis.
• The graph of x = a represents a straight line parallel to the Y-axis and the graph of y = a represent a straight line parallel to the X-axis.
• An equation of the type y = mx represents a straight line through the origin.

#### निम्नलिखित विकल्पों में कौन-सा विकल्प सत्य है, और क्यों? y=3x+5 का (i) एक अद्वितीय हल है (ii)केवल दो हल हैं (iii)अपरिमित रूप से अनेक हल हैं

(iii) अपरिमित रूप से अनेक हल हैं

क्योकि यह एक रैखिक समीकरण है और एक रेखा पर अपरिमित रूप से अनेक बिंदु होते हैं तथा प्रत्येक बिंदु इस रैखिक समीकरण का एक हल होता है।

#### Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Equation of two lines passing through (2,14) are given by: x+y=16 and 8x-y=2.
There are infinite number of lines that can pass through (2, 4) as infinite number of lines passes through a point.

#### If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

Given equation of line:
3y = ax + 7.

Putting x = 3 and y = 4,
we have, 3 × 4 = a × 3 + 7
⇒ 12 = 3a + 7
⇒ 12 – 7 = 3a
⇒ a = 5/3

#### निम्नलिखित समीकरण के चार हल लिखिए: 2x+y=7

2x + y = 7
⇒ y = 7 – 2x

x = 0 रखने पर, y = 7 – 2 × 0 = 7,
अतः, (0, 7) समीकरण का एक हल है।

x = 1 रखने पर, y = 7 – 2 × 1 = 5,
अतः, (1, 5) समीकरण का एक हल है।

x = 2 रखने पर, y = 7 – 2 × 2 = 3,
अतः, (2, 3) समीकरण का एक हल है।

x = 3 रखने पर, y = 7 – 2 × 3 = 1,
अतः, (3, 1) समीकरण का एक हल है।

इस प्रकार, (0, 7), (1, 5), (2, 3) और (3, 1) समीकरण 2x + y = 7 के चार हल हैं।

#### k का मान ज्ञात कीजिए जबकि x = 2, y = 1 समीकरण 2x + 3y = k का एक हल हो।

दिया है: x = 2, y = 1

2x + 3y = k में x = 2 और y = 1 रखने पर,
2 × 2 + 3 × 1 = k
⇒ k = 7

#### The taxi fare in a city is as follows: For the first kilometre, the fare is ₹ 8 and for the subsequent distance it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information.

Given that:
Distance traveled = x km and total fare = ₹ y

Total fare = Fare for first km + Fare for remaining distance

Therefore, the equation:
y = 8 + 5×(x – 1)
⇒ y = 5x + 3

#### 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).

Here, the cost of notebook = ₹ x and
the cost of pen =₹ y

According to question,
Cost of notebook = 2 × Cost of Pen
⇒ x = 2y
⇒ x – 2y = 0

#### Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c: 2x + 3y = 9.35.

2x + 3y = 9.35
⇒ 2x + 3y – 9.35 = 0

Hence,
Here a = 2, b = 3 and c = – 9.35.