NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 10 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Pair of Linear Equations in Two Variables |

Exercise |
Ex 3.5 |

Number of Questions Solved |
4 |

Category |
NCERT Solutions |

### NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

**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

3x – 9y – 2 = 0

**(ii)** 2x + y = 5

3x + 2y = 8

**(iii)** 3x – Sy = 20

6x – 10y = 40

**(iv)** x – 3y – 7 = 0

3x – 3y – 15 = 0

**Solution:**

**(iii)** Equations are 3x – 5y = 20 and 6x – 10y = 40

Here,

**
(iv) **Equations are x – 3y = 7 and 3x – 3y = 15

**Question 2.**

**(i)** for which values of a and b does the following pai of linea equation 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 equation have no solution₹

3x + y = 1

(2k – 1)x + (k – 1)y = 2k + 1

**Solution:**

**(i)** Equations are

⇒ a – 2b = 3 Solving (iii) and (iv) for a and b

**By cross multiplication method.**

**Question 3.**

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

8x + 5y = 9

3x + 2y = 4

**Solution:**

Equations are

**By coss multiplication Method :
**Equations are

**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.

**Solution:**

(i) Let fixed monthly hostel charges = and charges per day = ₹ y

A.T.Q.

As per condition of student A

x + 20y = 1000

As per condition of student B

x + 26y = 1180

By cross multiplication method

∴ Fixed monthly hostel charges = ₹ 400 and charges per day = ₹ 30

By cross multiplication method

Solving (i) and (ii) for x and y

By cross multiplication method

By cross multiplication method

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