$C=|x-6|+|x-10|+|x-2022|+|y-2019|$
Ta có: $\left | x-6 \right |\geq 0\forall x$
$\left | x-10 \right |\geq 0\forall x$
$\left | x-2022 \right |\geq 0\forall x$
$\left | y-2019 \right |\geq 0\forall y$
$\Rightarrow |x-6|+|x-10|+|x-2022|+|y-2019|\geq 0\forall x,y$
$\Leftrightarrow C\geq 0\forall x,y$
Dấu "=" xảy ra khi $\left\{\begin{matrix}
\left | x-6 \right |=0\\
\left | x-10 \right |=0\\
\left | x-2022 \right |=0\\
\left | y-2019 \right |=0
\end{matrix}\right.$
$\Leftrightarrow \left\{\begin{matrix}
x=6\\
x=10\\
x=2022\\
y=2019
\end{matrix}\right.$
Vậy $Min_{C}=0\Leftrightarrow \left\{\begin{matrix}
x=6\\
x=10\\
x=2022\\
y=2019
\end{matrix}\right.$
