Question

57/x+y + 6/x-y =10
38/x+y + 21/x-y=9​

Answer 1

57/x+y]+[6/x-y]=5 ......(1)

[57*(1/x+y)]+[6*(1/x-y)]=5

 

[38/x+y]+[21/x-y]=9 ......(2)

[38*(1/x+y)]+[21*(1/x-y)]=9

Let 1/x+y = A & 1/x-y = B

therefore,

57A+6B=5          .......(3)

38A=21B=9        .......(4)

Now,

(3)*7 & (4)*2

=

399A+42B=35

  76A+42B=18

(-)     (-)        (-)

___________

323A      = 17

A=17/323

A=1/19    .....(5)

 

put (5)in (4)=

38*(1/19)+21B=9

2+21B=9

21B=9-2

21B=7

B=7/21

B=1/3  ....(6)

1/x+y = A & 1/x-y = B=

x+y=1/A=19

x+y=19  ....(7)

x-y=1/B=3

x-y=3   ....(8)

Add (7)+(8)=

x+y=19

x -y=  3

______

2x = 22

x=11 &

y=8

hope this will help you.

thank you