Let the numbers be x and y. Set up our givens: x + y = 83 x - y = 17 Add equation (1) to equation (2) x + x + y - y = 83 + 17 The y-terms cancel out: 2x = 100 Divide each side by 2: 2x/2= 100/2 x = 50 Plug x = 50 into equation (1) 50 + y = 83 Subtract 50 from each side: 50 - 50 + y = 83 - 50 Cancel the 50 on the left side: y = 33 So our two numbers (x, y) = (33, 50)