Question

solve10/x+y +2/x+y=4 and 15/x+y _5/x_y =_2​

Answer 1

10/x+y +2/x-y=4________(1)

15/x+y-5/x-y=-2________(2)

let 1/x+y=A and 1/x-y=Bua

therefore eqn 1 and 2 will become

10A+2B=4

15A-5B=-2

Now multiplying eqn 1 by -5 and eqn 2 by 2 we get

-50A-10B=-20

30A-10B=-4

Now by elimination method we have A=16/80=1/5

and B=1

but 1/x+y=A and 1/x-y =B

putting the values of A and B we get x+y=5____(3) and x-y=1______(4)

Now from eqn 3 we get x=5-y Now putting the value of x in eqn 4 we get y=2 and x=5-y i.e x=5-2=3. Therefore x=3 and y=2

Answer 2

10/x+y +2/x-y=4      

15/x+y-5/x-y=-2      

let 1/x+y=u and 1/x-y=v

1) 10u+2v=4

2) 15u-5v=-2

Multiplying eqn 1 by 3 and eqn 2 by 2

30u+6v=12

30u-10v=-4

16v=16

v=1

u=2/10=1/5

3)1/x+y=1/5

x+y=5

4)1/x-y =1

x-y=1

Solving eqn 3 and 4 by elimination,

2x=6

x=3

y=2

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