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

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