**NCERT Solution For Class 10, Maths, Pair Of Linear Equations In Two Variables, Exercise 3.5 solutions** involves multiplications method to liner equations. This exercise have total four questions to study which are given below.

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Toggle## 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 **

**Ans:**

**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**

**Ans:**

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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**

**Ans:**

**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. **

**Ans:**

## 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**