#### description

- Graphical Method of Solving a System of Linear Equations

#### notes

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.

#### Video Tutorials

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

##### Series 1: playing of 2

#### Related QuestionsVIEW ALL [28]

Complete the following table to draw the graph of 3x - y = 2

x | ________ | -1 |

y | 1 | _______ |

(x,y) | ________ | _______ |