NCERT Notes for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Notes
Chapter Name  Pair of Linear Equations in Two Variables Notes 
Class  CBSE Class 10 
Textbook Name  NCERT Mathematics Class 10 
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 For any linear equation, each solution (x, y) corresponds to a point on the line. General form is given by ax + by + c = 0.
 The graph of a linear equation is a straight line.
 Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is: a_{1}x + b_{1}y + c_{1}= 0; a_{2}x + b_{2}y + c_{2} = 0 where a_{1}, a_{2}, b_{1}, b_{2}, c_{1} and c_{2} are real numbers, such that a_{1}^{2} + b_{1}^{2} ≠ 0, a_{2}^{2} + b_{2}^{2} ≠ 0.
 A pair of values of variables ‘x‘ and ‘y’ which satisfy both the equations in the given system of equations is said to be a solution of the simultaneous pair of linear equations.
 A pair of linear equations in two variables can be represented and solved, by
(i) Graphical method
(ii) Algebraic method
Graphical method
 The graph of a pair of linear equations in two variables is presented by two lines.
Algebraic methods
 Following are the methods for finding the solutions(s) of a pair of linear equations:
 Substitution method
 Elimination method
 Crossmultiplication method.
 There are several situations which can be mathematically represented by two equations that are not linear to start with. But we allow them so that they are reduced to a pair of linear equations.
Consistent system
 A system of linear equations is said to be consistent if it has at least one solution.
Inconsistent system
 A system of linear equations is said to be inconsistent if it has no solution.
Conditions for Consistency
Let the two equations be:
a_{1}x + b_{1}y + c_{1} = 0
a_{2}x + b_{2}y + c_{2} = 0
Then,