  We present a data-driven analysis of the resonant S-wave $\pi\pi \to \pi\pi$
and $\pi K \to \pi K$ reactions using the partial-wave dispersion relation. The
contributions from the left-hand cuts are accounted for in a model-independent
way using the Taylor expansion in a suitably constructed conformal variable.
The fits are performed to experimental and lattice data as well as Roy
analyses. For the $\pi\pi$ scattering we present both a single- and
coupled-channel analysis by including additionally the $K\bar{K}$ channel. For
the latter the central result is the Omn\`es matrix, which is consistent with
the most recent Roy and Roy-Steiner results on $\pi\pi \to \pi\pi$ and $\pi\pi
\to K\bar{K}$, respectively. By the analytic continuation to the complex plane,
we found poles associated with the lightest scalar resonances
$\sigma/f_0(500)$, $f_0(980)$, and $\kappa/K_0^*(700)$ for the physical pion
mass value and in the case of $\sigma/f_0(500)$, $\kappa/K_0^*(700)$ also for
unphysical pion mass values.
