$\left \{ {{2x-3y=7} \atop {3x+2y=4}} \right.$
$⇔\left \{ {{6x-9y=21} \atop {6x+4y=8}} \right.$
$⇔\left \{ {{6x-9y=21} \atop {6x+4y-6x+9y=8-21}} \right.$
$⇔\left \{ {{6x-9y=21} \atop {13y=-13}} \right.$
$⇔\left \{ {{6x-9y=21} \atop {y=-1}} \right.$
$⇔\left \{ {{6x+9=21} \atop {y=-1}} \right.$
$⇔\left \{ {{6x=21-9} \atop {y=-1}} \right.$
$⇔\left \{ {{6x=12} \atop {y=-1}} \right.$
$⇔\left \{ {{x=2} \atop {y=-1}} \right.$
