$\left \{ {{\frac{x}{y} =\frac{4}{6}} \atop {2x+3y=13}} \right.$
<=> $\left \{ {{6x=4y} \atop {2x+3y=13}} \right.$
<=> $\left \{ {{6x-4y=0} \atop {2x+3y=13}} \right.$
<=> $\left \{ {{6x-4y=0} \atop {6x+9y=39}} \right.$
<=> $\left \{ {{-13y=-39} \atop {2x+3y=13}} \right.$
<=> $\left \{ {{y=3} \atop {2x+3.3=13}} \right.$
<=> $\left \{ {{y=3} \atop {x=2}} \right.$
Vậy hệ phương trình có nghiệm : (x;y) = (2,3)
@Kem