See attachment for math work and answer. 
 
        
             
        
        
        
-7x - 2y = 19
4x + y = -12
Set y equal to each other (opposite signs are fine and you could also set x equal instead of y)
-7x - 2y = 19
8x + 2y = -76
Add equations together
x = -52
Plug x value into an equation
4(-52) + y = -12
Solve for y
-208 + y = -12
y = 196
Hope this helps! ;)
 
        
             
        
        
        
The fence must have two sides of length 45.45 ft and two sides of length 14.63
To cover each of 45.45 ft long side, he will need 45.45 /  2 = 22.7 slats which approximates to 23. So, they are 2 * 23 = 46 slats.
To cover each of 14.63 ft sides, he will need 14.63 / 2 = 7.3 which approximates to 8 (to not leave any spaces between each slat). So, they are 2 * 8 = 16 slats.
That makes 46 + 16 = 62 slats.
Answer: around 62 slats.
        
             
        
        
        
1,024 is 4^5 hope this helps :)