SSC (English Medium) Class 10th Board ExamMaharashtra State Board
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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.

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System of Linear Equations In two Variables by Graphical Method [00:06:59]
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