$\left \{ {{2x+2y=1} \atop {x-y=5}} \right.$
$⇒$ $\left \{ {{2x+2y=1} \atop {x=5+y}} \right.$
$⇔$ $\left \{ {{2(5+y)+2y=1} \atop {x=5+y}} \right.$
$⇔$ $\left \{ {{10+2y+2y=1} \atop {x=5+y}} \right.$
$⇔$ $\left \{ {{y=\dfrac{-9}{4}} \atop {x=5+y}} \right.$
$⇔$ $\left \{ {{y=\dfrac{-9}{4}} \atop {x=\dfrac{11}{4}}} \right.$
Vậy $(x;y)=(\dfrac{11}{4};\dfrac{-9}{4})$