Question

Solve 27/x+y-15x-y=-2 and 30/x+y-1/x-y=3

Answer 1

Answer:

x = 6 and y = 3

Step-by-step explanation:

27/(x+y) - 15/(x-y) = -2

30/(x+y) - 1/(x-y) = 3

let 1/(x+y) = a and 1/(x-y) = b

27a -15b = -2 ------------(1)

30a - b = 3 -------------(2)

multiply by 15 in eq. 2

450a - 15b = 45 -----------(3)

on subtract eq. 1 and 3

450a - 15b = 45

27a - 15b = -2

- + +

423a = 47

a = 47/423

a = 1/9

put a in eq 1

27a - 15b = -2

27(1/9) - 15b = -2

3 - 15b = -2

- 15b = -2 -3

- 15b = -5

b = -5/(-15)

b = 1/3

1/(x+y) = a and 1/(x-y) = b

1/(x+y) = 1/9 and 1/(x-y) = 1/3

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

x - y = 3 ------------(5)

on adding eq. 4 and 5

x + y = 9

x - y = 3

2x = 12

x = 6

put x in eq 4

x + y = 9

6 + y = 9

y = 9 - 6

y = 3