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