The Larger Of Two Numbers Exceeds Twice The Smaller By One. Three Times The Smaller Exceeds The Larger By Six. What Are The Two Numbers?

Let us make equations using the information given in the question above:

Supposing the larger number is x and the smaller number is y,

x = 2y + 1
and
3y = x + 6

You could also write:

x - 2y = 1
-x + 3y = 6

We can now solve these equations as a set of simultaneous equations:

  x - 2y = 1
- x + 3y = 6
  0  + y = 7
y = 7

To find x:

x - 2y = 1
x - 2(7) = 1
x - 14 = 1
x = 14 + 1
x = 15