Class 10, Maths, Chapter 3, Exercise 3.5, Solutions
Q.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; 3x – 9y – 2 = 0
(ii) 2x + y = 5; 3x + 2y = 8
(iii) 3x – 5y = 20; 6x – 10y = 40
(iv) x – 3y – 7 = 0; 3x – 3y – 15 = 0
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Q.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
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Q.3. Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9 ; 3x + 2y = 4
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Q.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 $\frac{1}{3}$when 1 is subtracted from the numerator and it becomes $\frac{1}{4}$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.
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NCERT Solutions For Class 10, Maths, Chapter 3, Pair Of Linear Equations In Two Variables (All Exercises)
- Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.1
- Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.2
- Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.3
- Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.4
- Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.5
- Class 10, Maths, Chapter 4, Pair Of Linear Equations In Two Variables, Exercise 3.6