2x - 5y =  1,      (1)
3x + 4y = 36.      (2)

Multiply equation (1) by 4 (both sides) and equation (2) by 5. You will get

 8x - 20y =   4,   (1')
15x + 20y = 180.   (2')

Now add (1') and (2') (both sides). In this way you eliminate "y" and get a single equation for "x":

8x + 15x = 4 + 180.

Simplify and solve it:

23x = 184,

x =  = 8.

Then from (2) 4y = 36 - 3*x = 36 - 3*8 = 12. Hence, y =  = 3.

Answer. x = 8, y = 3.