Решите систему уравнений lgx-lgy=2 x- 10y=900

lg(x/y)=2   x-10y=900   x/y=100 x-10y=900   x=100y   x=1000 90y=900   y=10

[latex]\left \{ {{lgx-lgy=2} \atop {x-10y=900}} \right.\\\left \{ {{lg(\frac{x}{y})=2} \atop {x-10y=900}} \right.\\\left \{ {{\frac{x}{y}=100} \atop {x-10y=900}} \right.\\\left \{ {{x=100y} \atop {100y-10y=900}} \right.\\\left \{ {{x=100y} \atop {90y=900}} \right.\\\left \{ {{x=1000} \atop {y=10}} \right.[/latex] Ответ: (1000;10)