An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables. A linear equation in two variables has infinitely many solutions.Some Properties of Linear Equations in Two Variables
(i) The graph of every linear equation in two variables is a straight line.
(ii) x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
(iii) The graph of x = a is a straight line parallel to the y-axis.
(iv) The graph of y = a is a straight line parallel to the x-axis.
(v) An equation of the type y = mx represents a line passing through the origin.
Every point on the graph of a linear equation in two variables is a solution of the linear equation. Moreover, every solution of the linear equation is a point on the graph of the linear equation.Graph of a Linear Equation in Two Variables
You know that each such equation has infinitely many solutions. How can we show them in the coordinate plane? You may have got some indication in which we write the solution as pairs of values. Example - x + 2y = 6 can be expressed in the form of a table as follows by writing the values of y below the corresponding values of x : Let us plot the points (0, 3), (2, 2), (4, 1) and (6, 0) on a graph paper. Now join any two of these points and obtain a line. Let us call this as line AB .