Pair of Linear Equations in Two Variables

Consider the following equation: 2x + 5 = 0
 the root of the equation is  `-5/2`. This can be represented on the number line as shown below:

While solving an equation, you must always keep the following points in mind.
The solution of a linear equation is not affected when: 

1. The same number is added to (or subtracted from) both sides of the equation. 
2. You multiply or divide both sides of the equation by the same non-zero number.
   So, any equation that can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables.

Linear equation is an algebraic equation having a degree of 1. We can say `2x+5=0` is a linear equation, as the degree of the variable x is 1. But in a linear equation in two variables have two variables. E.g. `2x+5y-1=0` is in the form of a linear equation with two variables, x and y. `ax+by+c=0` is a standard form of linear equation in two variables, where a is the coefficient of x, b is the coefficient of y, and c is a constant term, a, b and c are real numbers, also a and b are not equal to zero. 

In this chapter, we have to learn about the Pair of Linear Equations in Two Variables. Generally, A Pair of Linear Equations in Two Variables are written as `a_1x+b_1y+c_1=0` and `a_2x+b_2y+c_2=0.` Example `2x+9y+12=0` and `6x+1y+8=0` 
To learn how to solve A Pair of Linear Equations in Two Variables, there are two methods: Graphical and Algebraic. We will study this in the following concepts.