For a given quantity of gas, #(P_1V_1)/T_1 = (P_2V_2)/T_2#
Explanation:
Of course, when #P_1 =P_2#, we get Charles' Law, #V_1/T_1 = V_2/T_2#. And when #T_1=T_2#, we get Boyle's law, #P_1V_1 = P_2V_2#. Combining the two laws, we get #PV##=##k#. Once we introduce #n#, the molar quantity of gas, and a suitable constant, we get the Ideal Gas Law.