A cord is cut into two pieces of different lengths. the sum of the two lengths is 10 centimeters, and the difference between the two lengths is 4 centimeters. find the lengths of the two pieces of cord.

Start with x+y=10 and x-y=4
Add the equations to eliminate y:
    x+y=10 
 + x-y=4 
   2x =14 
So now solve for x:
    2x=14    (Divide each side by 2 to get x by itself)
     x=7 
Now you have solved for x, but you still need to solve for y:
   x+y=10
  7+y=10    (Subtract 7 from both sides to get y by itself)
    y=3 
Now you have both x and y but to check it, just plug it into the original equations:
    x+y=10 ---->  7+3=10   (That's correct)
     x-y=4 ---->  7-3=4   (That's correct) 
There's your final answer.