Question

solve: 2/x+y - 1/x-y =11 and 5/x+y + 4/x-y =8

Answer 1

2/x+y - 1/x-y =11 and 5/x+y + 4/x-y =8

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

Therefore, we get,

2u - 1v = 11 ..........(1)

5u + 4v = 8 ...........(2)

(1) × 4 + (2) gives,

8u - 4v = 44 ..........(3)

5u + 4v = 8 ...........(4)

(3) + (4) gives

13u = 52

u = 4

from (1) we get,

2u - 1v = 11

2(4) - 1v = 11

8 - v = 11

8 - 11 = v

v = -3

we have,

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

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

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

x - y = 1/-3 ..........(6)

(5) + (6) gives

2x = 1/4 - 1/3

2x = -1/12

x = - 1/24

from (5) we have,

x + y = 1/4

- 1/24 + y = 1/4

y = 1/4 + 1/24

y = 7/24

Hence the solution