solve for x and y please?

Question

8/x-9/y = 7

1/x+1/y = 1/6

Answer 1

8/x - 9/y = 7
1/x + 1/y = 1/6 (*8) = 8/x + 8/y = 4/3
8/x = 4/3 - 8/y

8/x = 7 + 9/y = 4/3 - 8/y
-4/3 -4/3
17/3 = -17/y
17 = 3(-17/y)
1 = -3/y
y = -3

1/x - 1/3 = 1/6
1/x = 1/6 +1/3 = 1/6 + 2/6 = 3/6 = 1/2
x = 2, y = -3

To confirm,
(8/2) - (9/-3) =
4 + 3 = 7

Answer 2

8/x-9/y = 7 ------- (1)
8(1/x) - 9(1/y)=7 -- (1)

1/x+1/y = 1/6 ---- (2)

1/x= 1/6 - 1/y ---- (2)

Sub (2) into (1)

8(1/6 - 1/y) - 9(1/y)=7
8/6 - 8/y - 9/y = 7
8/6 - (-1/y) = 7
8/6 + 1/y = 7
1/y = 7- 8/6
1/y = 17/3
3=17y
y = 3/17

when y = 3/17 using (2),

1/x+1/(3/17) = 1/6
1/x = 1/6 - 17/3
1/x = -11/2
x = -2/11

so y = 3/17 and x = -2/11

Answer 3

Subtract the second equation from the first one afterconverting the second equation second term 9/y:

8/x + 9/y = 7 ------8/x + 9/y = 7

(1/x + 1/y = 1/6)9 -----9/x + 9/y = 9/6

------------------------- -1/x + 0 = -33/6

multiply by x--------- -1 = -33x/6
hence 6/33 = x
solve for y----------- (33/6) + 1/y = 1/6
(33-1)/6 = 1/y

32/6 = -1/y
therefore y = -6/32