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or
6 2 3 ( 1 )

1

( 1 ) ( 13 ) 2 ( 1 ) ( 1 ) 3 ( 13 ) 6 u  u

 u  u

 u  u

x y

or
12 3

1

13 2 3 78 

 



x y

or
15

1

15 75

x y

?
15

1

15

x

, or 1

15

15

x

Again,
15

1

75

y

, or 5

15

75

y

? Solution (x,y) ( 1 , 5 )
Example 4. Solve by the method of cross-multiplication : 3 x 4 y 0
2 x 3 y  1
Solution : Given equations are :

¿

¾

½

 



2 3 1

3 4 0

x y

x y

or

¿

¾

½

 

 

2 3 1 0

3 4 0 0

x y

x y

By the method of cross-multiplication, we get,

( ) 3 ( 3 ) 2 ( 4 )

1

4 1 3 0 0 2 1 3 u  u

u  u

 u   u

x y

x y 1

2 3 1 2 3

3 4 0 3 4

 

 

or
9 8

1

4 0 0 3  



 

x y

or
1

1

4 3 





x y

or
1

1

4 3

x y

?
1

1

4

x

, or x 4

Again,
1

1

3

y

, or y 3

? Solution (x,y) ( 4 , 3 ).

Example 5. Solve by the method of cross-multiplication : 8
2 3

xy

(^33)
4
5 x y 
Solution : Arranging the given equations in the form axbyc 0 , we get,
x y 1 
2 13 3 2
1 1 6 1

  

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