Linear equation in two variable:  An equation in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero (a² + b² ≠ 0), is

called a linear equation in two variables x and y.

Solution of a linear equation in two variables:  Every solution of the equation is a point on the line representing it.

Each solution (x, y) of a linear equation in two variables, ax + by + c = 0, corresponds to a point on the line representing the equation, and vice versa.

Form of  linear equations in two variables:

The general form for a pair of linear equations in two variables x and y is

a₁x + b₁y + c₁ = 0 and

a₂x + b₂y + c₂ = 0,

Where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers and a₁² + b₁² ≠ 0, a₂² + b₂²  ≠ 0