Pairs of linear equation in two variable by asim rajiv shandilya 10th a

B Y - A S I M R A J I V S H A N D I L Y A
X T H A
Pairs of Linear Equation
in two Variable

Contents
 Introduction
 Graphical
Representation
 Algebraic Method
 Equation reducible to
pair of linear equation in
two variable.
 Summary

Equation
Linear
Equation in
One Variable
Linear
Equation in
Two Variable
Linear
Equation

Linear Equation In Two Variable
 Expressed using two
variable
 Can have infinite nos. of
solution
 General form of
representation is:-
 Here above a and b both
are non zero
 e.g. -

 Every linear equation can
be plotted on graph
 Each solution to a linear
equation correspond to a
point on line representing
the equation

Pair Of Linear Equation In Two Variable
 General form of
representation is:-
 They have same two
variable
 They can be solved by-
a)Graphically
b)Algebraically
*

Graphical Method
 Pair of linear equation in two variable is
represented by two lines. There are
three possibilities-
If lines
intersect at a
point
Consistent
equation
Unique
solution
If lines coincide Dependent
equation
Infinite solution
If lines are
parallel
Inconsistent
equation
No solution

In &
we have:-
Compare ratios Representation
Consistent equation
Parallel equation
Inconsistent Equation

Examples
 2x + 3y = 9 (1)
4x + 6y = 18 (2)
 These solutions are given
below:-
Table-1
x 0 4.5
3 0
x 0 3
3 1

Pairs of linear equation in two variable by asim rajiv shandilya 10th a

Algebraic Method
 There are three methods to find solution for
pair of linear equation in two variable-
a)Substitution method
b)Elimination method
c)Cross-multiplication method

Substitution Method
 Find value of 1st variable
in terms of 2nd variable in
either equation.
 Substitute the value of
1st variable in 2nd
equation& reduce it to
find value of 2nd variable.
 Now with value of 2nd
variable find out the
value of 1st variable

Examples
 7x – 15y = 2 (1)
x + 2y = 3 (2)
Then,
x + 2y = 3
x = 3 – 2y (3)
Now, Substitute the value of
x in Equation (1).
7(3 – 2y) – 15y = 2
21 – 14y – 15y = 2
– 29y = –19
Therefore, y =
Then, Substitute this value of
y in Equation (3)
x=

Elimination Method
 Make the coefficient of
any one variable in both
the equation common.
 Now add or subtract the
two equation to
eliminate the common
variable.
 Solve the equation to get
the value of 2nd variable.
 Now using the value of
2nd variable find the
value for 1st variable.

Examples
 9x – 4y = 2000 (1)
7x – 3y = 2000 (2)
Then, make the coefficients
of y equal.
27x – 12y = 6000 (3)
28x – 12y = 8000 (4)
Subtract Equation (3) from
Equation (4)
(28x – 27x) – (12y – 12y) =
8000 – 6000
x = 2000
(28x – 27x) – (12y – 12y) =
8000 – 6000
x = 2000
Substituting this value of x in
(1), we get
9(2000) – 4y = 2000
y = 4000

Cross Multiplication Method
 Write equations in
general form.
 Then express the
equations in following
way:-
 Find and provided

Examples
 2x + 3y – 46 = 0 (1)
3x + 5y – 74 = 0 (2)
Then,

Reducing an equation to Pair Of Linear Equation
In Two Variable
 This is done to equations
which are not in form:-
 For e.g. solving equation
such as given below:-
…these are not in general
form.

 In such case :-
 Now we get the equation
in general form i.e.
 Now solve the equation
using any method to get
p=2 , q=3.
 Substitute

Pairs of linear equation in two variable by asim rajiv shandilya 10th a

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