Class-10 : Maths - Chapter : 3 Pair Of Linear Equations In Two Variables (Ex-3.1Ex-3.2 Ex-3.3 Ex-3.4 Ex-3.5 Ex-3.6 Ex-3.7)
Pair of Linear Equations in Two Variables
In this chapter students will get to know the concept of Pair of Linear Equations in Two Variables. It explains how to represent a situation algebraically and graphically. Students will explore the methods of solving the pair of the linear equation through Graphical Method. This chapter describes the Algebraic Method, Elimination Method, Cross-Multiplication Method, Substitution Method respectively. Students must practice this chapter to master the method of solving the linear equations. The exercises present in the chapter should be dealt with utmost sincerity if one wants to score well in the examinations.
To download Ch-3 (Pair Of Linear Equations In Two Variables) solutions in PDF please click on the link below :
Ex - 3.1 : Download PDF
Ex - 3.2 : Download PDF
Ex - 3.3 : Download PDF
Ex - 3.4 : Download PDF
Ex - 3.5 : Download PDF
Ex - 3.6 : Download PDF
Ex - 3.7 (Optional) : Download PDF
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Points To Remember
1. Pair of linear equations in two variables - Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is :
a₁x + b₁y + c₁ = 0₁
a₂x + b₂y + c₂ = 0₂
where a₁,a₂,b₁,b₂,c₁,c₂ are real numbers, such that a₁² + b₁² ≠ 0 ; a₂² + b₂² ≠ 0
• The solution of a linear equation is a pair of values, one for x and one for y. This pair of values is called Ordered pair.
• A pair of values of x and y satisfying each of the equations in the given system of two simultaneous equations in x and y is called a solution of the system.
• A pair of linear equations will have either (a) a unique solution or (b) infinitely many solutions or (c) no solution.
3. A pair of linear equations in two variables can be represented, and solved, by the:
(i) Graphical method
(ii) Algebraic method
4. Graphical method : The graph of a pair of linear equations in two variables is represented by two lines;
(i) If the lines intersect at a point, the pair of equations is consistent.The point of intersection
gives the unique solution of the equations.
(ii) If the lines coincide, then there are infinitely many solutions. The pair of equations is consistent. Each point on the line will be a solution.
(iii) If the lines are parallel, the pair of the linear equations has no solution. The pair of linear equations is inconsistent.
Thus, corresponding to each solution (x, y) of the linear equation ax + by + c = 0, there exists a point on the line representing the equation ax + by + c = 0 and vice versa.
5. Algebraic Methods : There are three following methods for finding the solution(s) of a pair of linear equations :
(i) Substitution Method
(ii) Elimination Method
(iii) Cross-multiplication Method
6. If a pair of linear equations is given by a₁x + b₁y + c₁ = 0₁ & a₂x + b₂y + c₂ = 0₂ , then the following situations can arise :
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Exercise - 3.1
Exercise - 3.2
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Exercise - 3.3
Exercise - 3.4
Exercise - 3.5
Exercise - 3.6
Exercise - 3.7 (Optional)
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NBSE Solutions for Class 10 Maths for all Chapters by NBSE Guide Online are provided here. Just click on the chapter wise links given below :
• Chapter 6 Triangles
• Chapter 7 Coordinate Geometry
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Areas Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
The solution list comprises all the chapter-wise answers to the questions present in the NBSE book for Class 10 in a very precise and lucid manner, maintaining the objective of textbooks.
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