$\left \{ {{x-3y=2} \atop {-2x+5y=1}} \right.$
⇔$\left \{ {{x=2+3y} \atop {-2x+5y=1}} \right.$
⇔$\left \{ {{x=2+3y} \atop {-2(2+3y)+5y=1}} \right.$
⇔$\left \{ {{x=2+3y} \atop {-4-6y+5y=1}} \right.$
⇔$\left \{ {{x=2+3y} \atop {-y=5}} \right.$
⇔$\left \{ {{x=2+3y} \atop {y=-5}} \right.$
⇔$\left \{ {{x=2+3y=2+3.(-5)=-13} \atop {y=-5}} \right.$