Question

x-y/xy= 9 ; x+y/xy=5
( EQUATION REDUCIBLE)
SO FIND VALUE OF x AND y

Answer 1

Let 1/(x + y) = a and 1/(x - y) = b
 
therefore,
 
57a + 6b = 5 -------- (1)
38a + 21b= 9 -------- (2)
 
Solving equations 1 and 2, we get
 
A = 1/19    and b = 1/3
 
But 1/(x + y) = a and 1/(x - y) = b
 
⇒ (x + y) = 1/a = 19
 
⇒ x + y=19 -------- (3)
 
⇒ x - y = 1/b =3
 
⇒ x - y = 3 ----------(4)
 
Solving equations 3 and 4, we get x = 11 and  y = 8.

Answer 2

Given Equation is x - y/xy = 9

x - y = 9xy  ----- (1)

Given Equation is x + y/xy = 5

x + y = 5xy  ---- (2)


On solving (1) & (2), we get

x - y = 9xy

x + y = 5xy

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

2x = 14xy

y = 1/7.


Substitute y = 1/7 in (1), we get

x - y = 9xy

x - (1/7) = 9x(1/7)

x - 1/7 = 9x/7

7x - 1/7 = 9x/7

On cross-multiplication, we get

7(7x - 1)/7 = 9x 

49x - 7/7 = 9x

49x - 7 = 9x * 7(The value in the denominator will be moved to RHS - Right hand side).

49x - 7 = 63x

-14x = 7

x = -1/2.


Therefore the value of x = -1/2, y = 1/7.


Hope this helps!