NCERT class 10 maths chapter 3 Pair of Linear Equations in Two Variables
Question 1:Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (i) x – 3y – 3 = 0 (ii) 2x + y = 5 3x – 9y – 2 = 0 3x + 2y = 8 (iii) 3x – 5y = 20 (iv) x – 3y – 7 = 0 6x – 10y = 40 3x – 3y – 15 = 0
Exercise 3.5 maths class 10 Chapter 3 Pair of Linear Equations in Two Variables
Question 2:(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? 2x + 3y = 7 (a – b) x + (a + b) y = 3a + b – 2 (ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1 (2k – 1) x + (k – 1) y = 2k + 1
CBSE class 10 maths ncert solutions Chapter 3
Question 3:Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 3x + 2y = 4
Question 4:Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : (i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ` 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ` 1180 as hostel charges. Find the fixed charges and the cost of food per day. (ii) A fraction becomes 1 3 when 1 is subtracted from the numerator and it becomes 1 4 when 8 is added to its denominator. Find the fraction. (iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? (iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? (v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.