## Chapter 3: Pair of Linear Equations in Two Variables | NCERT Solutions

Pair of linear equations are the backbone of algebra and form the foundation for many advanced mathematical concepts. This chapter delves into the pair of linear equations in two variables.

This topic holds significant importance in the curriculum and has extensive real-world applications.

Understanding the intricacies of solving these equations will enhance our analytical skills and enable us to confidently tackle complex mathematical problems

** Linear equations in two Variables:**

An equation of the form ax + by + c = o where a, b, c are real numbers and (a^{2} + b^{2} ≠ 0) is called a linear equation in two variables.

** **Two linear equations in two variables of the same type are called a pair of linear equations in two variables.

a_{1}x + b_{1}y + c_{1} = 0 (a_{1}^{2} + b_{1}^{2 }≠ 0), a_{2}x + b_{2} y + c_{2} = 0 (a_{2}^{2} + b_{2}^{2}≠0); a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2} are real numbers

A pair of two linear equations can be solved by four methods

- Graphical method
- Substitution method
- Elimination method
- Cross multiplication method