Ch03. Pair of Linear Equations in Two Variables

In this self study course, you will learn Pair of linear equations in two variables and graphical method of their solution, consistency / inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. Simple problems on equations reducible to linear equations. For further understanding of concepts and for examination preparation, this course also has explanation of NCERT Exercise questions and practice questions based on the above topics are discussed in the form of assignments that have questions from Board’s Question Bank, RD Sharma, NCERT Exemplar etc. instead of only one book. The PDF of assignments can be downloaded within the course.

8 hours 12 minutes Course Duration
English Syllabus medium
Hindi + English Explanation
Not Logged in Enrollment status
The course duration is an approximation of the total length (duration) of all videos in the course, calculated automatically. Please report any errors to MathYug Support for prompt correction.

Course Content

Lecture – 1

Topics Covered

Meaning and introduction to Linear Equations in two variables

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.

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.

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.

Meaning of solution of Pairs of Linear Equation in two variables

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.

NCERT Exercise 3.2 Question 1 part (ii) 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.

Lecture – 2

Topics Covered

Graphical and Algebraical Tests for Parallel lines, intersecting lines and coincident lines

NCERT Exercise 3.2 Question 2 On comparing the ratios { \displaystyle \frac{a_1}{a_2}, \frac{b_1}{b_2}} and { \displaystyle \frac{c_1}{c_2}} find out whether the lines representing the
following pairs of linear equations intersect at a point, are parallel or coincident:

(i) 5x – 4y + 8 = 0
7x + 6y – 9 = 0

(ii) 9x + 3y + 12 = 0
18x + 6y + 24 = 0

(iii) 6x – 3y + 10 = 0
2xy + 9 = 0

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

 NCERT Exercise 3.2 Question 3 On comparing the ratios { \displaystyle \frac{a_1}{a_2}, \frac{b_1}{b_2}} and { \displaystyle \frac{c_1}{c_2}} find out whether the lines representing the
following pairs of linear equations are consistent, or inconsistent.

(i) 3x + 2y = 5
2x – 3y = 7

(ii) 2x – 3y = 8 ; 4x – 6y = 9

(iii) { \displaystyle \frac{3}{2}x + \frac{5}{3}y = 7; 9x-10y=14}

(iv) 5x – 3y = 11 ; – 10x + 6y = –22

(v) { \displaystyle \frac{4}{3}x + 2y = 8; 2x+3y=12}

 NCERT Exercise 3.2 Question 4 Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i) x + y = 5, 2x + 2y = 10

(ii) xy = 8,  3x – 3y = 16

(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0

(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

 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.

 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

PDF of Assignments
Assignment - 1
Assignment - 2