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Pair of Linear Equations in Two Variables
 Linear Equations in Two Variables
 Graphical Method of Solution of a Pair of Linear Equations
 Substitution Method
 Elimination Method
 Cross  Multiplication Method
 Equations Reducible to a Pair of Linear Equations in Two Variables
 Consistency of Pair of Linear Equations
 Inconsistency of Pair of Linear Equations
 Algebraic Conditions for Number of Solutions
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 Pair of Linear Equations in Two Variables
 Relation Between Coefficient
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 Quadratic Equations
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 Solutions of Quadratic Equations by Completing the Square
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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.
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Related QuestionsVIEW ALL [32]
Complete the following table to draw the graph of 2x – 6y = 3
x  5  x 
y  x  0 
(x,y)  (5,x)  (x,0) 
Complete the following table to draw the graph of 2x – 6y = 3:
x  −5  `square` 
y  `square`  0 
(x, y)  `square`  `square` 
Complete the following table to draw graph of the equations  (I) x + y = 3 (II) x – y = 4
x + y = 3
x 
3 

y  5  3  
(x,y)  (3,0)  (0,3) 
x – y = 4
x 

1  0 
y  0  4  
(x,y)  (0,4) 