# 3. Pairs of Linear Equations in Two Variables

##### 8+3 LECTURES

• This page has links to complete syllabus of NCERT Chapter 3 Pairs of Linear Equations in Two Variables based on syllabus recommended by CBSE based on class 10 maths.
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##### 3(A) || Exercise 3.1

00:00:26 Meaning and introduction to Linear Equations in two variables

00:05:09 NCERT Exercise 3.1 Question 1 Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

00:16:47 NCERT Exercise 3.1 Question 2 The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.

00:22:47 NCERT Exercise 3.1 Question 3 The cost of 2 kg of apples and 1kg of grapes on a day was found to be ₹160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically.

00:30:17 Meaning of solution of Pairs of Linear Equation in two variables

00:33:27 NCERT Exercise 3.2 Question 1 part (i) Form the pair of linear equations in the following problems and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

00:41:47 NCERT Exercise 3.2 Question 1 part (i) Form the pair of linear equations in the following problems and find their solutions graphically. (ii) 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen.

##### 3(B) || Exercise 3.2

00:00:30 Graphical and Algebraical Tests for Parallel lines, intersecting lines and coincident lines

00:05:22 NCERT Exercise 3.2 Question 2

00:13:32 Consistent and Inconsistent pair of linear equations in two variables (unique solution, no solution, infinite solution)

00:16:42 NCERT Exercise 3.2 Question 3

00:23:52 NCERT Exercise 3.2 Question 4

00:28:02 NCERT Exercise 3.2 Question 5 Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

00:33:42 NCERT Exercise 3.2 Question 6 Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines

00:36:42 NCERT Exercise 3.2 Question 7 Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

##### 3(C) || Exercise 3.3

Substitution Method 00:01:53 NCERT Exercise 3.3 Question 1

00:21:33 NCERT Exercise 3.3 Question 2 Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

00:25:03 NCERT Exercise 3.3 Question 3 part (i) The difference between two numbers is 26 and one number is three times the other. Find them.

00:28:03 NCERT Exercise 3.3 Question 3 part (ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

00:31:33 NCERT Exercise 3.3 Question 3 part (iii) The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. Later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball.

00:37:03 NCERT Exercise 3.3 Question 3 part (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

00:42:23 NCERT Exercise 3.3 Question 3 part (v) A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

00:48:03 NCERT Exercise 3.3 Question 3 part (vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

##### 3(D) || Exercise 3.4

Elimination Method 00:01:11 NCERT Exercise 3.4 Question 1

00:16:11 NCERT Exercise 3.4 Question 2 part (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction?

00:20:11 NCERT Exercise 3.4 Question 2 part (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

00:25:02 NCERT Exercise 3.4 Question 2 part (iv) Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

00:30:01 NCERT Exercise 3.4 Question 2 part (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

00:34:51 NCERT Exercise 3.4 Question 2 part (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

##### 3(E) || Exercise 3.5

CROSS MULTIPLICATION METHOD

00:00:55 NCERT Exercise 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 – 5y = 20 6x – 10y = 40 (iv) x – 3y – 7 = 0 3x – 3y – 15 = 0

00:13:55 NCERT Exercise 3.5 Question 2 part (i) (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

00:21:15 NCERT Exercise 3.5 Question 2 part (ii) (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

00:24:45 NCERT Exercise 3.5 Question 3 Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9 3x + 2y = 4

00:29:15 NCERT Exercise 3.5 Question 4 part (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.

00:34:25 NCERT Exercise 3.5 Question 4 part (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.

##### 3(F) || Exercise 3.6

00:00:36 NCERT Exercise 3.5 Question 4 part (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?

00:07:56 NCERT Exercise 3.5 Question 4 part (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?

00:17:36 NCERT Exercise 3.5 Question 4 part (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.

00:28:56 NCERT Exercise 3.6 Question 1 part (i)

00:34:26 NCERT Exercise 3.6 Question 1 part (ii)

##### 3(G) || HOTS & Important Questions

00:00:57 NCERT Exercise 3.6 Question 1 part (iii)

00:04:17 NCERT Exercise 3.6 Question 1 part (iv)

00:07:27 NCERT Exercise 3.6 Question 1 part (v)

00:11:07 NCERT Exercise 3.6 Question 1 part (vi)

00:15:17 NCERT Exercise 3.6 Question 1 part (vii)

00:20:57 NCERT Exercise 3.6 Question 1 part (viii)

00:28:27 NCERT Optional Exercise 3.7 Question 1 The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

##### 3(H) || Optional Exercise 3.7

00:01:27 NCERT Optional Exercise 3.7 Question 2 One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II]

00:08:57 NCERT Optional Exercise 3.7 Question 3 A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

00:17:17 NCERT Optional Exercise 3.7 Question 4 The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

00:27:27 NCERT Optional Exercise 3.7 Question 5 In a ∆ ABC, ∠ C = 3 ∠ B = 2 (∠ A + ∠ B). Find the three angles.

00:33:17 NCERT Optional Exercise 3.7 Question 8 ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral.

00:41:17 NCERT Optional Exercise 3.7 Question 7 part (i) (ii) (iii) (iv) (v)

00:01:03 NCERT Optional Exercise 3.7 Question 6