Question

solve the following for x and y.
(5/x-1) + (1/y-2)=2.
(6/x-1) - (3/y-2) =1

Answer 1

Heya !!!

5/ ( X-1) + (1/ Y-2) = 2 --------(1)

And,

( 6/ X -1) - ( 3/ Y-2) = 1 ----------(2)

Let 1/ X -1 = U and 1/Y-2 = V and put these values in equation (1) and (2) we get,

5U + V = 2 ---------(3)

And,

6U - 3V = 1 ----------(4)

From Equation (3) we get,

5U + V = 2

V = 2 - 5U ------(5)

Putting the value of V in equation (4) we get,

6U - 3V = 1

6U - 3 ( 2-5U) = 1

6U - 6 + 15U = 1

21U = 1 +6

21U = 7

U = 7/21 = 1/3

Putting the value of U in equation (5)

V = 2 - 5U = 2 - 5 × 1/3

V = 2 - 5/3 = 6 - 5/3 = 1/3

Now,

1/ X -1 = U

1/X - 1 =1/3

3= ( X -1)




X = 3+1



X = 4

And,

1/ Y -2 = V

1/Y -2 = 1/3

3 = Y -2

Y = 3+2

Y= 5

Hence,


X = 4 and Y = 5.

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