Charles' Law
" For a fixed mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature."
We have Ideal gas law PV = nRT
Dividing both sides by p, you will get
V/T = nR/P
Right hand side is constant
That means that V = constant x T, which is Charles' Law.
V1/ T1 = V2 / T2
Boyle's law
" The absolute pressure exerted by given mass of an ideal gas is inversely proportional to the volume it occupies if the
temperature and amount of gas remain unchanged within a closed system."
PV = n R T
According to Boyle's law n, T are constant. So Right hand side is some constant, let's say Z
PV = Z
So P1 V1 = P2 V2 { Boyle's Law }