linear equations in two variables Ncert solution class 9 maths chapter 4

Linear equations in two variables

Ncert solution class 9 maths chapter 4  

Linear equations in two variables EXERCISE 4.1

1. The cost of anotebook is twice the cost of a pen. Write a linear equation in two variablesto represent this statement. (Take the cost of a notebook to be Rs x and thatof a pen to be Rs y). 

2. Express thefollowing linear equations in the form ax + by + c = 0 and indicate the valuesof 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 

Linear equations in two variables EXERCISE 4.2 

1. Which one of the following options is true, and why? y = 3x + 5 has (i) aunique solution, (ii) only two solutions, (iii) infinitely many solutions 

2. Write foursolutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9(iii) x = 4y 

3. Check which of thefollowing 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) 

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

Ncert solution class 9 maths chapter 4.3 

1. Draw the graph ofeach of the following linear equations in two variables: (i) x + y = 4 (ii) x –y = 2 (iii) y = 3x (iv) 3 = 2x + y 

2. Give the equationsof two lines passing through (2, 14). How many more such lines are there, andwhy? 

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

4. The taxi fare in acity is as follows: For the first kilometre, the fare is Rs 8 and for thesubsequent distance it is Rs 5 per km. Taking the distance covered as x km andtotal fare as Rs y, write a linear equation for this information, and draw itsgraph. 

5. From the choicesgiven 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 4. Findthe value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y =k. 

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

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

8. In countries likeUSA and Canada, temperature is measured in Fahrenheit, whereas in countrieslike India, it is measured in Celsius. Here is a linear equation that convertsFahrenheit to Celsius: F = 9 C + 32 5  (i) Draw the graph of the linear equationabove using Celsius for x-axis and Fahrenheit for y-axis. (ii) If thetemperature is 30°C, what is the temperature in Fahrenheit? (iii) If thetemperature is 95°F, what is the temperature in Celsius? (iv) If thetemperature is 0°C, what is the temperature in Fahrenheit and if thetemperature is 0°F, what is the temperature in Celsius? (v) Is there atemperature which is numerically the same in both Fahrenheit and Celsius? Ifyes, find it. 

Linear equations in two variables  EXERCISE 4.4 

1. Give the geometricrepresentations of y = 3 as an equation (i) in one variable (ii) in twovariables 

2. Give the geometricrepresentations of 2x + 9 = 0 as an equation (i) in one variable (ii) in twovariables

Linear equations in two variables ncert solulution 

Ncert solution class 9 maths chapter 4