Graphical Method of Solution of a Pair 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 these equations on a graph, then the lines of this equation will intersect each other at some point.
In this condition, we can conclude

  1. We get an intersecting line.
  2. Such a type of pair of linear equations with two variables 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 equation is called a Consistent equation.


(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 these equations, the lines will coincide.
Thus, the conclusion in this condition is

  1. We get Consistent lines.
  2. Such a type of pair of linear equations with two variables where `a_1/a_2=b_1/b_2=c_1/c_2` have infinitely many solutions.
  3. This equation is also called a Consistent equation.


(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 parallel lines.
Here is the conclusion

  1. We will get parallel.
  2. Such a type of pair of linear equations with two variables 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 equation, which doesn't give any solution, is called an Inconsistent equation.
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Shaalaa.com | Pair of Linear Equation in two variable part 2 (Graphical Method)

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Pair of Linear Equation in two variable part 2 (Graphical Method) [00:11:49]
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