$\left \{ {{x+2y=-3} \atop {2x-y=4}} \right.$
⇔ $\left \{ {{2x+4y=-6} \atop {2x-y=4}} \right.$
⇔ $\left \{ {{5y=-10} \atop {x+2y=-3}} \right.$
⇔ $\left \{ {{y=-2} \atop {x+2.(-2)=-3}} \right.$
⇔ $\left \{ {{y=-2} \atop {x=1}} \right.$
Vậy HPT đã cho có nghiệm là: $\left \{ {{y=-2} \atop {x=1}} \right.$