$\left \{ {{\frac{27}{2x-y}+\frac{32}{x+3y}=7} \atop {\frac{45}{2x-y}-\frac{48}{x+3y}=-1}} \right.$
$Thay \frac{1}{2x-y}=t$ , $\frac{1}{x+3y}=u$
⇒$\left \{ {{27t+32u=7} \atop {45t-48u=-1}} \right.$
⇔$\left \{ {{81t+96u=21} \atop {90t-96u=-2}} \right.$
⇔$\left \{ {{171t=19} \atop {27t+32u=7}} \right.$
⇔$\left \{ {{t=\frac{1}{9}} \atop {27.\frac{1}{9}+32u=7}} \right.$
⇔$\left \{ {{t=\frac{1}{9}} \atop {u=\frac{1}{8}}} \right.$
$\text{Thế các giá trị của t, u vào lại $\frac{1}{2x-y}=t,\frac{1}{x+3y}=u$}$
⇒$\left \{ {{\frac{1}{2x-y}=\frac{1}{9}} \atop {\frac{1}{x+3y}=\frac{1}{8}}} \right.$
⇔$\left \{ {{2x-y=9} \atop {x+3y=8}} \right.$
⇔$\left \{ {{2x-y=9} \atop {-2x-6y=-16}} \right.$
⇔$\left \{ {{-7y=-7} \atop {x+3y=8}} \right.$
⇔$\left \{ {{y=1} \atop {x+3.1=8}} \right.$
⇔$\left \{ {{y=1} \atop {x=5}} \right.$
