Starting system:

1
2

x -

1
3

y = 5

1
3

x +

1
4

y = 9

It is often helpful to multiply each equation by a different number to prepare an "ADDITION" which will eliminate one of the 2 variables:

Multiply the top equation by 18
and the bottom equation by 24:

9x - 6y = 90
8x + 6y = 216

Add the terms in each column: 17x + 0y = 306
x = 18

Replace "x" with "18" in (e.g.) "9x - 6y = 90", to get:
9(18) - 6y = 90
9(18) - 90 = 6y
72 = 6y
y = 12