The difference between two numbers is 5. three times the larger number is equal to four times the smaller number plus 6. what are the two numbers

Let x and y represent the smaller and larger numbers, respectively.
  y - x = 5 . . . . . the difference is 5
  3y = 4x + 6 . . 3 times the larger is 4 times the smaller plus 6

Add x to the first equation to get an expression for y.
  y = x + 5
Use that in the second equation.
  3(x + 5) = 4x + 6
  3x + 15 = 4x + 6 . . . . . eliminate parentheses
  9 = x . . . . . . . . . . . . . . add -3x-6
  y = x+5 = 14

smaller number: 9
larger number: 14