If we let x be the first number and y be the second, we have (x + y) =13 and (2x - 3y) = 1.
From the first equation, we have x = (13- y). Substituting this into the second one, we have 2(13 - y) - 3y = 1.
Distributing the equation and re-arranging it, we now have (-5y) = (-26). Dividing both sides by -5, we have y = 5.
Now x = (13 - y) = 8.
Therefore, the two numbers are 5 and 8.
