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# NCERT solutions Mathematics Class 9 chapter 4 Linear Equations in two Variables

## Chapter 4 - Linear Equations in two Variables

#### Page 68

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).

Q 1 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- 2x+3y=9.3bar5

Q 2.1 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- x-y/5-10=0

Q 2.2 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:- –2x + 3y = 6

Q 2.3 | Page 68

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

Q 2.4 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

2x = –5y

Q 2.5 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

3x + 2 = 0

Q 2.6 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

y – 2 = 0

Q 2.7 | Page 68

Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c in case:-

5 = 2x

Q 2.8 | Page 68

#### Page 70

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

Q 1 | Page 70

Write four solutions for the following equation:- 2x + y = 7

Q 2.1 | Page 70

Write four solutions for the following equation:- πx + y = 9

Q 2.2 | Page 70

Write four solutions for the following equation:- x = 4y

Q 2.3 | Page 70

Check if (0, 2) is the solution of the equation x - 2y = 4.

Q 3.1 | Page 70

Check if (2, 0) is the solution of the equation x - 2y = 4.

Q 3.2 | Page 70

Check if (4, 0) is the solution of the equation x - 2y = 4.

Q 3.3 | Page 70

Check if (1, 1) is the solution of the equation x - 2y = 4.

Q 3.4 | Page 70

Check if (sqrt2", "4sqrt2) is the solution of the equation x - 2y = 4.

Q 3.5 | Page 70

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

Q 4 | Page 70

#### Page 74

Draw the graph of the following linear equations in two variables:- x + y = 4

Q 1.1 | Page 74

Draw the graph of the following linear equations in two variables:- x – y = 2

Q 1.2 | Page 74

Draw the graph of the following linear equations in two variables:- y = 3x

Q 1.3 | Page 74

Draw the graph of the following linear equations in two variables:- 3 = 2x + y

Q 1.4 | Page 74

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

Q 2 | Page 74

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

Q 3 | Page 74

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.

Q 4 | Page 74

From the choices given below, choose the equation whose graphs are given in the given figures.

For the first figure

(i) y = x

(ii) x y = 0

(iii) y = 2x

(iv) 2 + 3y = 7x

For the second figure

(i) y = x +2

(ii) y = x − 2

(iii) y = − x + 2

(iv) x + 2y = 6

Q 5 | Page 74

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

Q 6 | Page 74

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.

Q 7 | Page 74

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=(9/5)C+32

(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.

Q 8 | Page 74

#### Page 77

Give the geometric representations of y = 3 as an equation in one variable.

Q 1.1 | Page 77

Give the geometric representations of y = 3 as an equation in two variables.

Q 1.2 | Page 77

Give the geometric representations of 2x + 9 = 0 as an equation in one variable.

Q 2.1 | Page 77

Give the geometric representations of 2x + 9 = 0 as an equation in two variables.

Q 2.2 | Page 77

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