$\left\{{{2x-y=5}\atop{3x+2y=4}}\right.$
$\Leftrightarrow \left\{{{6x-3y=15}\atop{6x+4y=8}}\right.$
$\Leftrightarrow \left\{{{-7y=7}\atop{6x-3y=15}}\right.$
$\Leftrightarrow \left\{{{y=-1}\atop{6x+3=15}}\right.$
$\Leftrightarrow \left\{{{x=2}\atop{y=-1}}\right.$
$\Rightarrow (x; y)=(2; -1)$