Question

Solve the pair of equations by reducing them to a pair of linear equations.
6x + 3y = 6xy
2x + 4y = 5xy

Answer 1

Hi,

6x + 3y = 6xy

divide each term with xy ,

=>6/y + 3/x = 6 ---( 1 )

2x + 4y = 5xy

divide each term with xy , we get

=> 2/y + 4/x = 5 ---( 2 )



Let 1/x = a , 1/y = b

6/y + 3/x = 6 => 6b + 3a = 6 ---( 3 )

2/y + 4/x = 5 => 2b + 4a = 5 ----( 4 )

Do [ ( 3 ) - 3 × ( 4 ) ], we get

6b + 3a = 6

6b + 12a = 15
_____________

- 9a = -9

a = ( -9 )/( -9 )

a = 1

Substitute a = 1 in equation ( 4 ),

we get

2b + 4 = 5

2b = 5 - 4

b = 1/2

Therefore ,

1/x = a = 1 =>x = 1 ,

1/y = b = 1/2 => y = 2

I hope this helps you.

: )

Answer 2

HELLO DEAR,

GIVEN:-

6x + 3y = 6xy

=> 2x + y = 2xy------------( 1 )

2x + 4y = 5xy-----------( 2 )

form---------( 1 ) & ---------( 2 )

2x + y = 2xy

2x + 4y = 5xy

---------------------

-3y = -3xy

x = 1 [ put in -----( 1 )]

we get,

2(1) + y = 2(1)y

2y - y = 2

y = 2 , x = 1

I HOPE ITS HELP YOU DEAR,

THANKS