$\left \{ {{2x+y=1} \atop {3x-2y=12}} \right.$
⇔$\left \{ {{y=1-2x} \atop {3x-2y=12}} \right.$
⇔$\left \{ {{y=1-2x} \atop {3x-2(1-2x)=12}} \right.$
⇔$\left \{ {{y=1-2x} \atop {7x-2=12}} \right.$
⇔$\left \{ {{y=1-2x} \atop {x=2}} \right.$
⇔$\left \{ {{y=1-2.2} \atop {x=2}} \right.$
⇔$\left \{ {{y=-3} \atop {x=2}} \right.$