  In this article we consider a first-order completely integrable system of
partial differential equations $\partial \Fi/partial x=A(x, t) \Fi, \partial
\Fi/partial t=B(x, t) \Fi$ with $\Fi=(\fi_1, \fi_2)^{\tau}$ where $A(x, t)$ and
$B(x, t)$ are 2 by 2 holomorphic matrices functions. Under some assumptions we
find a variable change by which the system $\partial \Fi/\partial x=A(x, t)
\Fi$ is reduced to an equation independent on the variable $t$. As an
application we show that the R. Fuchs's conjecture for the Painlev\'e equations
is true for some algebraic solutions.
