$\left \{ {{2(x-2y)+3(x+2y)=4} \atop {(x-y)+2(x+y)=1}} \right.$
⇔$\left \{ {{2x-4y+3x+6y=4} \atop {x-y+2x+2y=1}} \right.$
⇔$\left \{ {{5x+2y=4} \atop {3x+y=1}} \right.$
⇔$\left \{ {{5x+2y=4} \atop {6x+2y=2}} \right.$
⇔$\left \{ {{-x=2} \atop {6x+2y=2}} \right.$
⇔$\left \{ {{x=-2} \atop {6.-2+2y=2}} \right.$
⇔$\left \{ {{x=-2} \atop {y=7}} \right.$
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