# Pair of Linear Equations in Two Variables

This chapter begins with a brief introduction of the pair of linear equations in two variables and the ways of solving them: Graphical and Algebraic. A detailed methodology is given for the Graphical method and examples are shown to give a better understanding. The algebraic methodology has three main methods namely -Substitution, Elimination, and Cross Multiplication Method. Step by step procedures, formulae, examples, and word problems are explained for each of the three methods. The linear equations are then checked for consistency and inconsistency. The focus then shifts to how linear equations have a variety of applications.

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## Graphical Techniques

- Graphically Solving a Pair of Linear Equations
- Special Cases
- Overview of Graphical Approach
- Relationships between Coefficients of Nature of Solutions