Do yours exactly step-by-step like this one:

2x - y = 8, x + 4y = -5

Solve the 2nd equation for x:

  x + 4y = -5
     -4y     -4y
----------------
  x      = -5-4y

Substitute (-5-4y) for x in the 1st equation:

       2x - y = 8
 2(-5-4y) - y = 8
 -10 - 8y - y = 8
     -10 - 9y = 8
     +10      +10
-----------------
         -9y = 18
       
           y = -2
       
Substitute (-2) for y in

       x = -5-4y 
       x = -5-4(-2)
       x = -5+8
       x = 3

The solution is (x,y) = (3,-2)

Edwin