Solve the system using elimination:
5x+4y=12
3x-3y=18
show step-by-step instructions

Okay, first thing is you want to have x and y all alone. So you need to solve the equations. 
Equation 1:
5x+4y=12 (you want to subtract 5x on both sides to get y on one side and x on the other)

5x+4y=12
-5x           -5x
     4y=12-5x    (Now if you want x and y alone you want to divide 4 on both sides)
     4
y=3-1.25x Now that's you equation

Equation 2: (Basically the same steps for the 1st equation)
3x-3y=18  (Subtract 3x on both sides)
-3x         -3x 
-3y=18-3x     (Now you divided by -3 on both sides)
       -3
y=-6+x     (you might notice why is there only 1 x, well because -3 divided by -3 is going to be a positive 1. You can either put a "x" or a 1x, doesn't really matter).

now since you have the two equations simplified you want to solve by doing multi-step. 

3-1.25x=-6+x (Now you want to add 1.25x so you can get rid of the negative x)
  +1.25x     +1.25x
        3=  -6+2.25  (Remember x alone is like 1, so it's like 1+1.25, next you want to add 6 on both sides. So you have a number and a variable all alone).

3=-6+2.25x
+6  +6
9    =  2.25x    (Next you divided 2.25 on both sides)
2.25    2.25

 
x =4 
If your not sure, you can plug in or replace x with 4. :D 
I really do hope this help you understand :D