50 БАЛЛОВ!!! Помогите решить, пожалуйста, с подробным решением

Question 1

Question 2

1)
$\left \{ {{log_2 (x+y)=3} \atop {log_{15} x=1-log_{15} y}} \right.$
ОДЗ: $x\ \textgreater \ 0; y\ \textgreater \ 0; x\ \textgreater \ -y$

$\left \{ {{log_2 (x+y)=log_2 2^3} \atop {log_{15} x=log_{15} 15-log_{15} y}} \right.$
$\left \{ {{log_2 (x+y)=log_2 8} \atop {log_{15} x=log_{15} \frac{15}{y}}} \right.$
$\left \{ {{x+y= 8} \atop {x=\frac{15}{y}}} \right.$
$\left \{ {{\frac{15}{y}+y= 8} \atop {x=\frac{15}{y}}} \right.$
$\left \{ {{\frac{15+y^2-8y}{y}= 0} \atop {x=\frac{15}{y}}} \right.$
$\left \{ {{y^2-8y+15= 0} \atop {x=\frac{15}{y}}} \right.$
$\left \{ {{(y-3)(y-5)= 0} \atop {x=\frac{15}{y}}} \right.$

$\left \{ {{y=3} \atop {x=\frac{15}{y}}} \right.$
$\left \{ {{y=3} \atop {x=\frac{15}{3}=5}} \right.$

$\left \{ {{y=5} \atop {x=\frac{15}{5}=3}} \right.$
Два решения - (3,5) и (5,3)
2)
$\left \{ {{log_3 (xy)=2+log_3 2} \atop {log_3 (x+y)=2}} \right.$
ОДЗ: $xy\ \textgreater \ 0; x\ \textgreater \ -y$

$\left \{ {{log_3 (xy)=log_3 9+log_3 2} \atop {log_3 (x+y)=log_3 9}} \right.$
$\left \{ {{log_3 (xy)=log_3 18} \atop {log_3 (x+y)=log_3 9}} \right.$
$\left \{ {{xy=18} \atop {x+y= 9}} \right.$
$\left \{ {{xy=18} \atop {x= 9-y}} \right.$
$\left \{ {{(9-y)y=18} \atop {x= 9-y}} \right.$
$\left \{ {{9y-y^2-18=0} \atop {x= 9-y}} \right.$
$\left \{ {{(3-y)(y-6)=0} \atop {x= 9-y}} \right.$

$\left \{ {{y=3} \atop {x= 9-y}} \right.$
$\left \{ {{y=3} \atop {x= 9-3=6}} \right.$

$\left \{ {{y=6} \atop {x= 9-y}} \right.$
$\left \{ {{y=6} \atop {x= 9-6=3}} \right.$

Два решения - (6,3) и (3,6)

Question 3

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