Question

if 6x +3y= 6xy and 2x+4y=5xy find the value of x and y

Answer 1

Hii friend,

6X +3Y = 6XY........(1)

2X +4Y = 5XY.......(2)

On dividing each equations by XY , we get

6/Y + 3/X = 6.........(3)

2/Y +4/X = 5........(4)


Putting 1/X = U and 1/Y = V in equation (3) and (4).

6V + 3U = 6.........(5)

2V +4U = 5..........(6)


From equation (5) we get,

6V +3U = 6

6V = 6-3U

V = 6-3U/6.......(7)


Putting the value of V in equation (6)

2V + 4U = 5

2 × (6-3U/6) +4U = 5

6-3U/3 + 4U = 5

6-3U + 12U = 5 × 3

9U +6 = 15

9U = 15-6

U = 9/9 = 1

Putting the value of U in equation (7)

V = 6-3U/6 = 6-3×1/6 = 6-3/6 = 3/6 = 1/2

Therefore,

1/X = U

1/X => 1 = X = 1


And,

1/Y = V

1/Y = 1/2 => Y = 2.

HOPE IT WILL HELP YOU.... :-)