Linear Equations in two variables-Notes

An equation of the form ax + by + c = 0 where a, b, c are real numbers, a ≠ 0, b ≠ 0 and x, y are variables is called a linear equation in two variable.

Anys pair of values ofxandywhich satisfies the equation ax + by + c = 0, wherea, b, c are non-zero real numbers, is called a solution of the equation

•   A linear equation in two variables has infinitely many solutions.

•   Every point on the graph of a linear equation in two variables is a solution of the equation.

Geometric representation of       ax + c = 0 as an equation

•   in one variable is

•   in two variable is

       a.x + 0.y = –c.

•   If a ≠ 0, c ≠ 0 and b = 0.

       The equation

       ax + by + c �� 0 reduces to ax + c = 0 or

       The graph is a straight line. Parallel to y-axis and passing through the point

•   If b ≠ 0, c ≠ 0 and a ≠ 0. The equation

       ax + by + c = 0 reduces to by + c = 0 or The graph is a straight line parallel to x axis and passing through the point

•   If a ≠ 0, b ≠ 0, c = 0 . The equation ax + by + c = 0 reduces to ax = 0 i.e.       x= 0. The graph is y-axis itself

•   If a = 0, b ≠ 0, c = 0. The equation ax + by + c = 0 reduces to by = 0 i.e.       y= 0. The graph is x-axis itself

•   If c = 0 , the equation ax + by + c = 0 reduces to ax + by = 0. The graph is a line passing through origin.