untitled

8

2 3



x y

or 8
6

3 2

x y

or 3 x 2 y 48 0

Again, 3 3

4

5

 y 

x

or 3

4

5 12



x y

or 5 x 12 y 12 0

? the given equations are : 3 x 2 y 48 0
5 x 12 y 12 0
By the method of cross-multiplication, we get,

3 12 5 2

1

2 12 12 48 48 5 12 3 u  u

 u  u

u ( )u( ) ( ) ( )

x y

x y 1

5 12 12 5 12

3 2 48 3 2

 



or
36 10

1

24 576 240 36  

 



x y

or
46

1

552 276 





x y

or
46

1

552 276

x y

?
46

1

552

x

or, 12

46

552

x

Again,
46

1

276

y

, or 6

46

276

y

? Solution (x,y) ( 12 , 6 )

Verification of the correctness of the solution :

Putting the values of xandy in given equations, we get,

In 1st equation, L.H.S. = 6 2
3

6

2

12

2 3

  

x y

8 R.H.S.

In 2nd equation, L.H.S. = 3 6
4

5 12

3

4

5

 u

u

 y

x

15  18  3 = R.H.S.
? the solution is correct.
Example 6. Solve by the method of cross-multiplication : axby ab bxay.
Solution : Given equations are

¿

¾

½





bx ay ab

ax by ab

or,

¿

¾

½

 

 

0

0

bx ay ab

ax by ab

By the method of cross-multiplication, we get,