NCERT Solutions Class 9 Mathematics Chapter 4 Linear Equations In Two Variables Download In Pdf

Chapter 4 Linear Equations In Two Variables Download in Pdf

**Question 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 Rs x and that of a pen to be Rs y).

**Question 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:

(i) 2x + 3y = 9.35

(ii) x –
5
y – 10 = 0

(iii) –2x + 3y = 6

(iv) x = 3y

(v) 2x = –5y (

vi) 3x + 2 = 0

(vii) y – 2 = 0

(viii) 5 = 2x

**
Question 1.**Which one of the following options is true, and why?
y = 3x + 5 has

(i) a unique solution

(ii) only two solutions

(iii) infinitely many solutions

**Question 2.** Write four solutions for each of the following equations:

(i) 2x + y = 7

(ii) πx + y = 9

(iii) x = 4y

**Question 3.** Check which of the following are solutions of the equation x – 2y = 4 and which are
not:

(i) (0, 2)

(ii) (2, 0)

(iii) (4, 0)

(iv) ( 2 , 4 2)

(v) (1, 1)

**
Question 4**. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

EXERCISE 4.3

**
Question 1.** Draw the graph of eachof the following linear equations in two variables:

(i) x + y = 4

(ii) x – y = 2

(iii) y = 3x

(iv) 3 = 2x + y

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

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

**
Question 4.** The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the
subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total
fare as Rs y, write a linear equation for this information, and draw its graph.

**
Question 5.** From the choices given below, choose the equation whose graphs are given in Fig. 4.6
and Fig. 4.7.
For Fig. 4. 6 For Fig. 4.7

(i) y = x

(i) y = x + 2

(ii) x + y = 0

(ii) y = x – 2

(iii) y = 2x

(iii) y = –x + 2

(iv) 2 + 3y = 7x

(iv) x + 2y = 6

**
Question 6.** If the work done by a body on application of a constant force is directly proportional
to the distance travelled by the body, express this in the form of an equation in two
variables and draw the graph of the same by taking the constant force as 5 units. Also
read from the graph the work done when the distance travelled by the body is
(i) 2 units (ii) 0 unit

**Question 7.** Yamini and Fatima, two students of Class IX of a school, together contributed Rs 100
towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear
equation which satisfies this data. (You may take their contributions as Rs x and
Rs y.) Draw the graph of the same.

**
Question 8.** In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in
countries like India, it is measured in Celsius. Here is a linear equation that converts
Fahrenheit to Celsius:
F =
9 C + 32
5

(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.

(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?

(iii) If the temperature is 95°F, what is the temperature in Celsius?

(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?

(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

EXERCISE 4.4

**
Question 1.** Give the geometric representations of y = 3 as an equation

(i) in one variable

(ii) in two variables

**
Question 2.** Give the geometric representations of 2x + 9 = 0 as an equation

(i) in one variable

(ii) in two variables

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- Chapter 3 Coordinate Geometry
- Chapter 4 Linear Equations In Two Variables
- Chapter 7 Triangles
- Chapter 8 Quadrilaterals
- Chapter 9 Areas of Parallelograms and Triangles
- Chapter 10 Circles
- Chapter 11 Constructions
- Chapter 12 Heron’s Formula
- Chapter 13 Surface Areas and Volumes
- Chapter 14 Statistics
- Chapter 15 Probability

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