Linear Equations in Two Variables
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. The solution of a linear equation is not affected when:
a) the same number is added to (or subtracted from) both the sides of the equation.
b) both the sides of the equation are multiplied or divided by the same non-zero number.
A linear equation in two variables is represented geometrically by a straight line whose points make up the collection of solutions of the equation. This is called the graph of the linear equation.
The polynomial equation ax + by + c = 0 is called a linear equation because its geometrical representation is a straight line.
To obtain the graph of a linear equation in two variables, it is enough to plot two points corresponding to two solutions and join them by a line. However, it is advisable to plot more than two such points so that you can immediately check the correctness of the graph.
The equation of y-axis is x = 0, and the equation of x-axis is y = 0.
The graph of x = a is a straight line parallel to the y-axis.
The graph of y = a is a straight line parallel to the x-axis.
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.