CBSE Class 10 Mathematics Chapter 3 - Pairs of linear equations in two variables - summery

CBSE Class 10 Mathematics  Chapter 3 - Pairs of linear equations in two variables - Summery

In this chapter, we have covered the following key points:

1. Methods for Solving Pairs of Linear Equations:

1. Graphical Method
2. Algebraic Method

2. Graphical Method: When dealing with a pair of linear equations in two variables, we can represent them graphically, resulting in two lines on a coordinate plane.

• If the lines intersect at a single point, this point represents the unique solution for the pair of equations. This is indicating that the pair of equations is consistent.
• If the lines coincide, it implies that there are infinite solutions, as every point on the line is a valid solution. This is indicating that the pair of equations is dependent (consistent).
• If the lines are parallel and never intersect, the pair of equations has no solution, making them inconsistent.

3. Algebraic Methods: We have explored two primary algebraic methods for finding solutions to pairs of linear equations:

1. Substitution Method
2. Elimination Method

4. Conditions for Consistency: When a pair of linear equations is expressed in the form         a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, following situations can arise:

• When 

the pair of linear equations is consistent.

• When

the pair of linear equations is inconsistent.

• When

the pair of linear equations is dependent and consistent.

5. Transformation of Non-linear Equations: We've observed that various real-world situations can be mathematically represented by non-linear equations, which can be adjusted and manipulated to reduce them to a pair of linear equations.

Understanding these methods and concepts is essential when working with pairs of linear equations in two variables, as they provide powerful tools for solving practical problems in various fields, including mathematics, science, and engineering.