Question

solve 8/x+y+2/x-y =3 and 3/x+y -1/x-y =1/4​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

x = 3 and y = 1

Step-by-step explanation:

8/x+y + 2/x-y = 3

Take 1/x+y as A and 1/x--y as B

--> 8a + 2b = 3 ----(1)

3/x+y - 1/x-y = 1/4

--> 3a - b = 1/4. (take 4 to the Lhs)

--> 12a - 4b = 1 ----(2)

Eliminate (1) and (2)

(1) × 2

16a + 4b = 6

12a - 4b = 1

__________

28a = 7

----------------

----> a = 7/28 = 1/4

from (2)

-4b = 1 - 12×1/4

-b = -2/4. ==> b = 1/2

Substitution:

A = 1/x+y = 1/4 (by reciprocal)

a = x+y = 4 ------(3)

B = 1/x-y = 1/2

b = x-y = 2 -----(4)

Eliminate (3) and (4)

x + y = 4

x - y = 2

------------

2x = 6

_______

===> x = 3

y = 4 - 3 = 1

Therefore, x = 3 and y = 1

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