\(\frac{\text{x}}{2}\) - \(\frac{\text{y}}{5}\) = 1 - - - - - - 1

y - \(\frac{\text{x}}{3}\) = 8 - - - - - 2

We clear the fractions by multiplying through by the lcm of 2 and 5 = 10 for eqn 1 and 3 for eqn 2

5x - 2y = 10 - - - - - - - 3

3y - x = 24 - - - - - - - - - 4

from eqn 4, make x the subject of formula

x = 3y - 24 (after multiply thru by -1, so x can be positive)

Put x = 3y - 24 into eqn 3

5(3y - 24) - 2y = 10

15y - 120 - 2y = 10

15y - 2y = 10 + 120

13y = 130

y = \(\frac{130}{13}\) = 10

y = 10 put in eqn 4

3y - x = 24 - - - - - - - - - 4

3(10) - x = 24

30 - x = 24

- x = 24 - 30 = -6

x = 6 ( minus cancels out minus)

Therefore, x = 6, y = 10.