Title Class 9 Mathematics Chapter 4 Linear Equations.pdf ✅

Linear Equations in Two Variables DPP-01 [Topic: Linear Equations] Very Short Answer Type Questions 1. Express the following linear equations in the form aaaa + bbbb + cc = 0 and indicate the values of aa, bb and cc in each case. (i) + = 2.5 (ii) 2 = −5 (iii) − 3 = 0 (iv) 2 + 3 = 0 (v) 7 = 9 (vi) −2 + 3 = 6 2. Write each of the following as an equation in two variables. (i) 3 = 5 (ii) = 2 (iii) = −3 2 (iv) 5 = 9 2 (v) − 1 2 = 2 3. Express the given equation as a linear equation in two variables in standard form: √3 = 2 4. Express the following statements in the form of a linear equation in two variables. (i) The cost of a half dozen eggs are the same as the cost of one packet of bread. (ii) Riya got 3 4 of the cake, Tanya got. (iii) The cost of a key ring is ₹5 less than the twice of the cost of a pen. (iv) The sum of the ordinate and abscissa of a point is 8. Short Answer Type Question 5. The number of sincere students ( ) in a class is two more than twice the number of careless students (y). Write a linear equation in two variables for this situation. How does sincerity help and carelessness harm a student?
Linear Equations in Two Variables DPP-02 [Topic: Solution of a Linear Equation] Very Short Answer Type Questions 1. Find a solution of the equation −5xx + 2yy = 14. 2. Is xx = 5, yy = −2 a solution of the linear equation 2xx − yy = 12 ? 3. What is a solution of linear equation yy = 2xx if xx = 3 2 ? 4. A linear equation has solutions (−5,5), (0,0) and (5, −5). Write the linear equation. 5. Find the solution of the linear equation 2xx + 0yy = 9. Short Answer Type Questions-I 6. For what value of kk, xx = 2 and yy = −1 is a solution of xx + 3yy − kk = 0. 7. Express yy in terms of xx, given that 2xx − 5yy = 7. Check whether the point (−3, −2) is on the given line. 8. For what value of cc, the linear equation 2xx + cc = 8 has equal values of xx and yy as its solution? 9. Find the value of kk if the line represented by the equation 2xx − kk = 9 passes through the point (−1, −1). 10. If the point (2,1) lies on the line 5xx − 2yy = 2kk, find ' kk '. Also find one more solution for the given equation. 11. If (2,0) is a solution of the linear equation 2xx + 3yy = kk, then find the value of kk ? 12. If the point (3,4) lies on the graph of 3xx = aa + 7, then find the value of aa. Short Answer Type Questions-II 13. Find mm, if point (7, −3) lies on the equation yy − 3 7 = mm �xx − 2 7 � 14. Find any three solutions for the equation 15xx − 2yy = 7. 15. When 5 times the larger of the two numbers is divided by the smaller, the quotient and remainder are 2 and 9, respectively. Form a linear equation in two variables for above and give its two solutions. [Imp.] 16. If xx = 2, yy = −1 is a solution of the equation aa − yy = 5, find the value of aa. Also find two more solutions of the equation. 17. If xx = 2kk − 1 and yy = kk is a solution of the equation 3xx − 5yy − 7 = 0, find the value of kk. 18. If xx = 2αα + 1 and yy = αα − 1 is a solution of the equation 2xx − 3yy + 5 = 0, find the value of αα.
19. One of the solutions of the equation 8xx − aa + aa2 = 0 is given by xx = 1 and yy = 6. Find the value of aa. 20. Solve for xx: 3 xx−1 + 1 xx+1 = 4 xx , where xx ≠ 0, xx ≠ 1, xx ≠ −1. 21. Solve for xx: (5xx + 1)(xx + 3) − 8 = 5(xx + 1)(xx + 2) Long Answer Type Questions 22. The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation: C = 5F − 160 9 (i) If the temperature is 86∘ F what is the temperature in Celsius? (ii) If the temperature is 35∘ C, what is the temperature in Fahrenheit? (iii) 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? (iv) What is the numerical value of the temperature which is same in both the scales? 23. Solve: 4 5 �xx + 5 6 � − 2 3 �xx − 1 4 � = 1 1 6 24. ₹ 27 is in the form of 50 paise, 25 paise and 20 paise coins. The number of 25 paise coins is double the number of 20 paise coins but half the number of 50 paise coins. Find the number of coins of each type. 25. A student studying in a university covers his expenditure on daily needs and tuition fee by driving a taxi on rent in the city. The taxi fare in the city is as follows: For the first kilometre the fare is ₹40 and for the subsequent distance it is ₹20 per kilometre. (i) Write a linear equation for the given information by taking different variables for the distance covered and total fare. (ii) Which mathematical concept is used in above problem? (iii) Which value is depicted by the student by driving a taxi? 26. On her birthday, Natasha donated 4 toffees each to children of an orphanage and 20 chocolates to adults working there. Taking the total items distributed as xx and the number of children yy, write a linear equation in two variables for the above situation. (i) Write the equation in standard form. (ii) How many children are there if total 80 items were distributed? (iii) What values does Natasha possess?