solve the simultaneous equation

Question

5xy/(x+y) = 6

4xz/(x+z) = 3

3yz/(y+z) = 2

Answer 1

5xy/(x+y)=6

5xy = 6(x+y)

(x+y)/xy = 5/6

1/y + 1/x = 5/6 .......(1)

 

 

Similarly,

(x+z)/xz = 4/3

1/z + 1/x = 4/3 ........(2)

 

(y+z)/zy = 3/2

1/z + 1/y = 3/2 ........(3)

 

Adding equations (1), (2) and (3):

 

2/x + 2/y + 2/z = 5/6 + 4/3 + 3/2

2(1/x + 1/y + 1/z) = 11/3

1/x + 1/y + 1/z = 11/6  .......(a)

 

Replacing equation (1) in (a):

5/6 + 1/z = 11/6

z = 1

 

Replacing equation (2) in (a):

4/3 + 1/y = 11/6

1/y = 3/6

y = 2

 

Replacing equation (3) in (a):

3/2 + 1/x = 11/6

1/x = 2/6

x = 3