$\left \{ {{2x+3y=4} \atop {4x-y=1}} \right.$
$\Leftrightarrow$ $\left \{ {{2x+3y=4} \atop {12x-3y=3}} \right.$
$\Leftrightarrow$ $\left \{ {{2x+3y=4} \atop {12x-3y=3}} \right.$
$\Leftrightarrow$ $\left \{ {{14x=7} \atop {12x-3y=3}} \right.$
$\Leftrightarrow$ $\left \{ {{x=\frac{1}{2}} \atop {12.\frac{1}{2}-3y=3}} \right.$
$\Leftrightarrow$ $\left \{ {{x=\frac{1}{2}} \atop {y=1}} \right.$
$\Rightarrow (x;y)=(\frac{1}{2}; 1)$