Using Dalton's law of partial pressures
Dalton's law of partial pressures means that the total pressure in the final volume $V=V_1+V_2$ is equal to the sum of the partial pressures P(N2) + P(Ar) in this volume. However, the partial pressure of N2 in the total volume $V$ is not the same as the pressure of N2 in its initial volume $V_1$. You have to account for the expansion. This probably means you also need to use the ideal gas law for that.