$\left \{ {{2x+5y=-13} \atop {-5x+6y=-23}} \right.$
⇔ $\left \{ {{10x+25y=-65} \atop {-10x+12y=-46}} \right.$
⇔ $\left \{ {{37y=-111} \atop {2x+5y=-13}} \right.$
⇔ $\left \{ {{y=-3} \atop {2x+5.(-3)=-13}} \right.$
⇔ $\left \{ {{y=-3} \atop {2x=2}} \right.$
⇔ $\left \{ {{y=-3} \atop {x=1}} \right.$
Vậy hệ có nghiệm duy nhất $(x;y)=(1;-3)$