Question

10÷x+y+2÷x-y=4;15÷x+y-5÷x-y=-2​

Answer 1

Answer:

10/x+y +2/x-y=4

15/x+y-5/x-y=-2_

(1)

let 1/x+y=A and 1/x-y=Bua therefore equation 1 and 2 will become 10A+2B=4

15A-5B=-2

282 *

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 equation 4 we get y2 and x=5-y i.e x=5-2=3. Therefore x=3 and y=2

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Answer 2

Answer _ Therefore, X=3, y=2 is the solution of our equation

Explanation-

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

15/X+y _ 5/x_y = 2 -----(2)

Let 1/X+y = u

and 1/x_y = v

So, our equations become

10u +2v = 4 ----(3)

15u _ 5v = _2 ----(4)

Now, we solve

10u + 2v = 4 ----(3)

15u_5v = _2 ----(4)

From (3)

10u+2v = 4

10u = 4_2v

u = 4_2v/10

Putting the value of u in (4)

15u _ 5v = _2

15(4_2v)/10 _5v =_2

Multiplying both side by 2*3 (4_2v)/2 _2*5v = 2*_2

3(u_2v) 10v = _4

12_6v_10v =_4

_16v = _6v

v= _16/_16

v= 1

Putting v= 1 in (3)

10u +2v = 4

10u + 2 (1) = 4

10 u + 2 = 4

10u = 4_2

10 u = 2

u = 2/10

u = 1/5

Hence, u= 1/5 and v= 1

But, we need to find X and y

u = 1/x+y

1/5 = 1/x+y

x+y = 5

v= 1/x_y

1= 1/x_y

x_y

So our equations become

x+y = 5 ----(5)

x_y = 1 ---(6)

Adding (5) and (6)

(x+y) + (x_y). = 5+1

2x= 6

x = 6/2

x= 3

Putting value of Y in (5)

x+y = 5

Putting value of Y in (5)

x+y = 5

3 + y = 5

y= 5_3

y= 2

Therefore, X= 3 and y = 2 is the solution of our equation