Verified answer

[tex]\displaystyle\bf\\ODZ:\\\\x+y > 0 \ \ \ \Rightarrow \ \ \ x > -y\\\\\\\left \{ {{\log_{\sqrt{2} }(x+y)=2 } \atop {3^{6-x} }\cdot 4^{y+3} =36} \right. \\\\\\\left \{ {{x+y=(\sqrt{2} )^{2} } \atop {3^{6-x} }\cdot 4^{y+3}=3^{2} \cdot 4 } \right. \\\\\\\left \{ {{x+y=2} \atop {6-x=2 \ \ ; \ \ y+3=1}} \right. \\\\\\\left \{ {{x+y=2} \atop {x=4 \ \ ; \ \ y=-2}} \right. \\\\\\\left \{ {{4-2=2-verno} \atop {x=4 \ \ ; \ \ y=-2}} \right. \\\\\\Otvet: \ (4 \ ; \ -2)[/tex]