The Sum Of Two Numbers Is 51. Their Difference Is 13. What Is The Smaller Of The Two Numbers?

Let x = the larger number
     y = the smaller number
x + y = 51
x - y = 13 ==> x = y + 13
substitute y + 13 back into the first equation and solve for y
(y + 13) + y = 51
  2y + 13 = 51
2y + 13 - 13 = 51 - 13
  2y = 38
  2y/2 = 38/2
  y = 19
substitute 19 for y back into either equation
  x - 19 = 13
  x - 19 + 19 = 13+ 19
  x =  32
substitute both x and y values back into other equation as a check
32 + 19 = 51
  51 = 51
so, the larger number, x = 32, and the smaller number, y = 19

The answer is 19.