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8 y - 3 x = 5 x y --- equation (1)

6 y - 5 x = - 2 x y ---- equation (2)

multiply (1) by 2 and multiply (2) with 5 and then add,

16 y - 6 x + 30 y - 25 x = 10 x y - 10 x y

46 y - 31 x = 0

so y = 31/46 * x --- (3)

substitute this value of y in (1).

8 * 31/46 x - 3 x = 5 x * (31/46 x)

multiply by 46 and divide by x :

248 - 138 = 155 x

x = 110 / 155 = 22/31

y = 31/46 * 22/31 = 11/23

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Divide equations (1) and (2) by xy:

8 / x - 3 / y = 5 and 6 / x - 5 / y = - 2

call 1/x = X and 1/y = Y

8 X - 3 Y = 5 --- (3)

6 X - 5 Y = -2 --- (4)

24 X - 9 Y - 24 X + 20 Y = 15 + 8

11 Y = 23

=> Y = 23 /11

substitute this in (3)

8 X - 3 * 23 /11 = 5

8 X = 5 + 69/11 = 124/11

X = 31/22