lets work with the equations system:
(2/5)x + y = 12
(5/2)y - x = 6
first lets eliminate the fractions multiplying by a suitable number, 5 and 2, each equation:
2x + 5y = 60
5y - 2x = 12
rearrange and add the equations:
2x + 5y = 60
-2x + 5y = 12
------------------
0 + 10y = 72
10y = 72
now we have eliminated the x variable and can solve the system