{ lg(x^2-x^2)=1 { x-y=2 Решите систему уравнений

ОДЗ:
x²-y²>0
(x-y)*(x+y)>0
$\left \{ {{x-y\ \textgreater \ 0} \atop {x+y\ \textgreater \ 0}} \right. , \left \{ {{x\ \textgreater \ y} \atop {x\ \textgreater \ -y}} \right.$
или
$\left \{ {{x-y\ \textless \ 0} \atop {x+y\ \textless \ 0}} \right. , \left \{ {{x\ \textless \ y} \atop {x\ \textless \ -y}} \right.$
$\left \{ {{lg( x^{2} - y^{2} )=1} \atop {x-y=2}} \right. \left \{ {{ x^{2} - y^{2} = 10^{1} } \atop {x-y=2}} \right.$
$\left \{ {{(x-y)*(x+y)=10} \atop {x-y=2}} \right. \left \{ {{2*(x+y)=10} \atop {x-y}=2} \right.$
$\left \{ {{x+y=5} \atop {x-y=2}} \right. +$
2x=7, x=3,5
$\left \{ {{x=3,5} \atop {y=1,5}} \right.$