Pair of Linear Equations in Two Variables:
Linear equations in two variables can be represented in the form of Ax + By = C, where A, B, and C are constants, and x and y are variables. When we have two linear equations in two variables, we call it a pair of linear equations.

Important Definitions & Formulas:
1. Solution of a Pair of Linear Equations: The solution to a pair of linear equations is the values of x and y that satisfy both equations simultaneously.
2. Consistent System: A system of linear equations that has at least one solution is called a consistent system.
3. Inconsistent System: A system of linear equations that has no solution is called an inconsistent system.
4. Dependent System: A system of linear equations that has infinitely many solutions is called a dependent system.
5. Independent System: A system of linear equations that has a unique solution is called an independent system.

Explanation:
When we have a pair of linear equations in two variables, we can solve them using various methods such as substitution, elimination, or graphing. The goal is to find the values of x and y that satisfy both equations simultaneously. Depending on the nature of the equations, the system can be consistent, inconsistent, dependent, or independent.
It is important to understand the properties and solutions of a pair of linear equations to effectively solve problems in algebra and real-life situations. Mastering this concept will help in developing problem-solving skills and logical reasoning abilities.