Question

solve 9/x+y-5/x-y=4 where x+y is not equal to zero and x - y is not equal to zero

Answer 1

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

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