Question

Solve: 4/x+y - 3/x-y =5
9/x+y - 5/x-y = 4 where x+y =0 and x-y is not equal to 0​

Answer 1

Answer:

4/x+y - 3/x-y = 5 ....(1)

9/x+y - 5/x-y = 4 ....(2)

Let 1/x+y = a, 1/x-y = b

⇒ 4a - 3b = 5...(1)

9a - 5b = 4...(2)

Multyply equation (1) with' 5 'and equation (2) with' 3'

we get:

20a - 15b = 25..(1)

27a - 5b  = 12...(2)

By subtracting ...(2) from (1) we get:

-7a = 13

a= -13/7

a = 1/x+y = -13/7

⇒x+y = -7/13

substituting the value of 'a' in 4a - 3b = 5, we get:

4(-13/7) - 3b = 5

-52/7 - 3b = 5

b =( 5 + 52/7)÷ -3

b = -29/7

b= 1/x-y = -29/7

⇒x-y = -7/29

∴ x+y = -7/13 ....(3)

x-y =  -7/29 ....(4)

by adding (3) and (4):

2x = -7/13 -7/29

x = - 294/ 377

substitute the value of 'x' in (3):

-294/377 + y = -7/13

y= -7/ 13 + 294/377

y= 91/ 377

⇒ x= -294/377 =-42/ 53

y= 91/377 = 13/53

∴ x= -42/53 , y = 13/53

Hope it helps :)

Answer 2

Given  :   4/x+y - 3/x-y =5 9/x+y - 5/x-y = 4 where x+y  and x-y is not equal to 0​

To find  :  Value of x & y

Solution:

4/(x+y) - 3/(x-y) =5  

9/(x+y) - 5/(x-y) = 4

Let say  1/(x + y)  =  a

& 1/(x - y)  = b

4a  - 3b  = 5      Eq1

9a  - 5b  = 4     Eq2

=> 3*eq2   - 5 * eq1

=> 27a  - 20a  = 12   - 25

=> 7a = -13

=> a = -13/7

9*eq1  - 4 * eq2

=> -27b  + 20b =  45 - 16

=> -7b = 29

=> b  = -29/7

1/(x + y) = -13/7

=> x + y  = -7/13

1/(x - y)  = -29/7

=> x - y  = -7/29

2x  = -7/13 - 7/29

=> 2x =  -7 * 42/(13 * 29)

=> x  = - 147/377

2y  = -7/13  + 7/29

=> 2y =  7(-29 + 13)/(29 * 13)

=> y = -56/377

x  = - 147/377 ,  y = -56/377

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