# 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 free PDF to downloads updated for academic session 2020-21 following new NCERT Books. UP Board Solutions for Class 9 Maths Chapter 4 Prashnavali 4.1, Prashnavali 4.2, Prashnavali 4.3 and Prashnavali 4.4 are given below in Hindi Medium. View UP Board Solution and NCERT Solutions for 2020-21 in Video Format Hindi Medium and English Medium or free download in PDF or use it as online all the digital contents. There is not any login or registration condition. Just visit to website and use the contents free of cost.

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## NCERT Solutions for Class 9 Maths Chapter 4

 Class: 9 Maths (English and Hindi Medium) Chapter 4: Linear Equations in Two Variables

### 9th Maths Chapter 4 Solutions in English & Hindi Medium

NCERT Solutions for Class 9 Maths Chapter 4 all exercises are given below. NCERT Solutions 2020-21 are updated for the CBSE Exams 2021 based on Latest CBSE Syllabus 2020-2021. NCERT Solutions and UP Board Solutions for Class 9 Maths Chapter 4 as 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.

• ### Study Material

#### Class 9 Maths Chapter 4 Exercise 4.1 Solution in Video

Class 9 Maths Chapter 4 Exercise 4.1 Solution
Class 9 Maths Exercise 4.1 Question wise Solution

#### Class 9 Maths Chapter 4 Exercise 4.2 Solution in Video

Class 9 Maths Exercise 4.2 Question 1, 2 Solution
Class 9 Maths Exercise 4.2 Question 3, 4 Solution

Class 9 Maths Chapter 4 Exercise 4.2 Solution
Class 9 Maths Chapter 4 Exercise 4.3 Solution

#### Class 9 Maths Chapter 4 Exercise 4.3 Solution in Video

Class 9 Maths Exercise 4.3 Question 1, 2 Solution
Class 9 Maths Exercise 4.3 Question 3, 4 Solution

Class 9 Maths Exercise 4.3 Question 5, 6 Solution
Class 9 Maths Exercise 4.3 Question 7 Solution

#### Class 9 Maths Chapter 4 Exercise 4.4 Solution in Video

Class 9 Maths 4 Exercise 4.4 Question wise Solution
Class 9 Maths Chapter 4 Exercise 4.4 Solution
##### When is the solution of a linear equation is not affected?

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.

##### What is meant by a solution of the linear equation?

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.

#### Important Notes on 9th Maths Chapter 4

• 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.
##### Important Point in 9th Maths Chapter 4
1. 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.
2. 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.
3. An equation of the type y = mx represents a straight line through the origin.

### Important Questions on 9th Maths Chapter 4

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.                