  A combination of measurements of the inclusive top-quark pair production
cross-section performed by ATLAS and CMS in proton-proton collisions at
centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The
cross-sections are obtained using top-quark pair decays with an opposite-charge
electron-muon pair in the final state and with data corresponding to an
integrated luminosity of about 5 fb$^{-1}$ at $\sqrt{s}=7$ TeV and about 20
fb$^{-1}$ at $\sqrt{s}=8$ TeV for each experiment. The combined cross-sections
are determined to be $178.5 \pm 4.7$ pb at $\sqrt{s}=7$ TeV and
$243.3^{+6.0}_{-5.9}$ pb at $\sqrt{s}=8$ TeV with a correlation of 0.41, using
a reference top-quark mass value of 172.5 GeV. The ratio of the combined
cross-sections is determined to be $R_{8/7}= 1.363\pm 0.032$. The combined
measured cross-sections and their ratio agree well with theory calculations
using several parton distribution function (PDF) sets. The values of the
top-quark pole mass (with the strong coupling fixed at 0.118) and the strong
coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from
the combined results by fitting a next-to-next-to-leading-order plus
next-to-next-to-leading-log QCD prediction to the measurements. Using a version
of the NNPDF3.1 PDF set containing no top-quark measurements, the results
obtained are $m_t^\text{pole} = 173.4^{+1.8}_{-2.0}$ GeV and
$\alpha_\text{s}(m_Z)= 0.1170^{+ 0.0021}_{-0.0018}$.
