class 10th graphical method in linear equations

linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.

The constants may be numbers, parameters, or even non-linear functions of parameters, and the distinction between variables and parameters may depend on the problem.

(Linear equations can have one or more variables)

A linear equation is an equation between two variables that gives a straight line when plotted on a graph.

Linear Equation: An equation of the form ax+by+c=0 or ax+by =d, where a,b,c,d are real numbers, a²+b² ≠0 and x, y are variables, is called linear equation in two variables. 

Pair of linear equations in two variables:
i)Graphical method 
(a) If 

         

     

 then graph will represent two interesting lines. Point of intersection is solution of the system.

(b) If 

 then graph will represent two parallel lines. System has no common solution.

(c)If

 then graph will represent two coinciding lines. System has infinitely many solutions.

ii)Algebraic method

Let the system of linear equation in two variables be a₁x+b₁y=c₁ and a₂x+b₂y=c₂.

(a) If 

 
then system has a unique solution and is known as consistent.
(b) If

(          then system has no solution and is known as inconsistent.

(c) If
                                                      

(          then system has infinitely many solutions and is known as dependent consistent.