The pressure temperature relationship for an ideal gas, known as Amontons law or Gay Lussac's law should be obtainable from Boyle's and Charles's laws.
I did the following.
For a given sample of an ideal gas, by Boyle's law,
And by Charle's law
Where $b,a$ are constants for the given sample of gas. Substituting for $V$ in the first equation from the second,
Which is not the correct relationship. Pressure should be directly proportional to temperature. Where did I go wrong?