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CBSE Pair of Linear Equations in Two Variables Class 10th Formulas

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Linear  equation in two variable 

Solution of a linear equation 

 x = α,γ = β is a solution of the linear equation ax + by + c = 0, if aα + bβ + c = 0. Each solution (α, β) of a linear equation in two variables ax + by + c = 0 corresponds to a point on the line representing the equation in a Cartesian plane and vice versa. 

Pair of linear equations in two variables or system of simultaneous linear equation in two variables

 Solution of system of simultaneous equation in two variables :

A pair of values of x and y satisfying each in a given system is called solution of given system . 

Methods  of  solving  a  pair  of  linear  equations  in  two  variables:

There are two methods for solving a pair of linear equations in two variables.

1.  Graphical Method   2. Algebraic Method

1.Graphical  Method

Plot the graph of two equations in x and y in cartesian plane onthe same graph.

(a)  If  two  lines  intersect,  then  the  solution  is  unique  andequations are consistent.

(b)  If  two  lines  are  parallel,  then  there  is  no  solution  andequations are inconsistent.

(c) If two lines are coincident, then there are infinitely many solutions and equations are consistent.

2.  Algebraic    Method:   

There  are  three  methods  for  finding solution  of  a  pair  of  linear  equations  (i)  Substitution  method

(ii) Elimination method (iii) Cross-multiplication method.

Cross – multiplication method : If the given system is 

This helps us in  memorising  the solution which is given as under :

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