$\begin{Bmatrix}
3x-\left | y \right |=1\\
5x+3y=11
\end{Bmatrix}\\\Leftrightarrow \left\{\begin{matrix}
3x-\left | y \right |=1\\
x=\dfrac{11}{5}-\frac{3}{5}y
\end{matrix}\right.\\\Leftrightarrow 3\left ( \dfrac{11}{5}-\dfrac{3}{5}y \right )-\left | y \right |=1\\\Leftrightarrow y=2\\\Leftrightarrow x=\dfrac{11}{5}-\dfrac{3}{5}.2\\\Leftrightarrow x=1$
Vậy $(x,y)=(1,2)$