untitled

Solution by the method of elimination :

Conveniently, one equation or both equations are multiplied by such a number so
that after multiplication, absolute value of the coefficients of the same variable
become equal. Then as per need, if the equations are added or subtracted, the
variable with equal coefficient will be eliminated. Then, solving the obtained
equation, the value of the existing variable will be found. If that value is put
conveniently in any of the given equations, value of the other variable will be found.

(3) Method of cross-multiplication :
We consider the following two equations :

..........( )

...........()

0 2

0 1

2 2 2

1 1 1

 

 

ax by c

ax by c

Multiplying equation (1) by b 2 and equation (2) by b 1 , we get,

.........( )

.........()

0 4

0 3

21 12 12

12 12 21

 

 

abx bby bc

abx bby bc

Subtracting equation (4) from equation (3), we get

..........( 5 )

1

or,

or,( )

( ) 0

12 21 12 21

12 21 12 21

12 21 21 12

bc bc ab ab

x

ab ab x bc bc

ab ab x bc bc





 

  

Again, multiplying equation (1) by a 2 and equation (2) by a 1 , we get,

.........()

.........()

0 7

0 6

1 2 12 21

1 2 21 12

 

 

aax aby ca

aax aby ca

Subtracting equation (7) from equation (6), we get

..........( 8 )

1

or,

or, ( ) ( )

( ) 0

1 2 2 1 12 21

12 21 12 21

21 12 1 2 2 1

ca ca ab ab

y

ab ab y ca ca

ab ab y ca ca





   

  

From (5) and (8) we get,

12 21 12 21 12 21

1

ca ca ab ab

y

bc bc

x







From such relation between xand y, the technique of finding their values is called
the method of cross-multiplication.
From the above relation between xandy, we get,