10.9 Given $x$ and $y$ as real numbers, solve the equation

$$
(-5+2 i) x-(3-4 i) y=2-i
$$
10.9 By expanding the brackets in the left part of the equation and grouping the real and imaginary parts, we have $(-5 x-3 y)+(2 x+4 y) i=2-i$.

Now, using the condition of equality of two complex numbers (10.2), we obtain the system

$\left\{\begin{array}{l}5 x+3 y=-2 \\ 2 x+4 y=-1\end{array}\right.$

from which $x=-\frac{5}{14}, y=-\frac{1}{14}$.

Answer: $x=-\frac{5}{14}, y=-\frac{1}{14}$.