**Ex 3.5 Class 10 Maths Question 1.**

Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions. In case there is 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

**Solution for Ex 3.5 Class 10 Maths Question 1**

**Solution for Ex 3.5 Class 10 Maths Question 1**

**Ex 3.5 Class 10 Maths 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)

**Solution for Ex 3.5 Class 10 Maths Question 2**

**Solution for Ex 3.5 Class 10 Maths Question 2**

**Ex 3.5 Class 10 Maths Question 3.**

Solve the following pair of linear equations by the substitution and cross-multiplication methods:

8x + 5y = 9, 3x + 2y = 4

**Solution for Ex 3.5 Class 10 Maths Question 3**

**Solution for Ex 3.5 Class 10 Maths Question 3**

**Ex 3.5 Class 10 Maths 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 Rs. 1000 as hostel charges, whereas a student B, who takes food for 26 days, pays Rs. 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 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.

**Solution for Ex 3.5 Class 10 Maths Question 4**

**Solution for Ex 3.5 Class 10 Maths Question 4**