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Graphical Method of Solution of a Pair of Linear Equations

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  • Graphical Method of Solving a System of Linear Equations

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In this method there are three conditions


(1)Condition- `a_1/a_2` is not equal to `b_1/b_2`


Example- `2x+9y+12=0` and `6x+1y+8=0` 


`2/6` is not equal to `9/1` 


If we represent this equations on graph then the lines of this equation will intersect each other at some point.
In this condition we can conclude-
1) We get Intersecting line.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2` is not equal to `b_1/b_2` have only one solution i.e unique solution.
3) This type of equations are called Consistent equations.


(2)Condition- `a_1/a_2`= `b_1/b_2`= `c_1/c_2`


Example- `2x+4y+8=0` and `6x+12y+24=0`


`2/6=1/3, 4/12=1/3, 8/24=1/3` i.e `1/3=1/3=1/3`


In the graphical representation of this equations the lines wil Coincide.
Thus the conclusion in this condition is-
1) We get conincent lines.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2=b_1/b_2=c_1/c_2` have infinitely many soultions.
3) This equation is also called as Consisitent equations.


(3) Condition- `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2`


Example- `2x+3y+4=0` and `4x+6y+7=0`


`2/4=1/2, 3/6=1/2, 4/7` i.e `1/2=1/2` is not equal to `4/7`

 

The graphical representation of these equations will result in parellel lines.
Here the conclusion is- 
1) We will get Parellel.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2` have no solution.
3) This type of Linear equations which dont give any solution are called as Inconsistent equations.

Shaalaa.com | Pair of Linear Equation in two variable part 2 (Graphical Method)

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