ОЧЕНЬ СРОЧНО!ПОМОГИТЕ)Решите логарифмическую систему уравнений на фото

ОДЗ: x>0 и у>0 [latex] \left \{ {{log_3(x+2y)=1} \atop {lgx+lgy=0}} \right. \ \ \textless \ =\ \textgreater \ \ \left \{ {{x+2y=3} \atop {lg(xy)=0}} \right. \ \ \textless \ =\ \textgreater \ \ \left \{ {{x+2y=3} \atop {xy=10^0} \right. \ \ \textless \ =\ \textgreater \ \ \left \{ {{x=3-2y} \atop {(3-2y)y=1}} \right. \\ \\ (3-2y)y=1 \\ 3y-2y^2=1 \\ 2y^2-3y+1=0 \\ \\ y_1=1 \\ y_2=0.5 \\ \\ x_1=3-2y_1=3-2*1=1 \\ x_2=3-2y_2=3-2*0.5=2 \\ \\ OTBET: \ (1;1); \ (2;0.5)[/latex]