$\left \{ {{x-2y=4} \atop {3x+y=6}} \right.$
⇔$\left \{ {{x=4+2y} \atop {3(4+2y)+y=6}} \right.$
⇔$\left \{ {{x=4+2y} \atop {12+6y+y=6}} \right.$
⇔$\left \{ {{x=4+2y} \atop {6+7y=0}} \right.$
⇔$\left \{ {{x=4+2(\frac{-6}{7})} \atop {y=\frac{-6}{7} }} \right.$
⇔$\left \{ {{x=\frac{16}{7}} \atop {y=\frac{-6}{7} }} \right.$