Answer:
x = 2, y = 3
Step-by-step explanation:
[tex]Domain:\ x>0\ \wedge\ x\neq1\ \wedge\ y>0 \wedge\ y\neq1\\\\\underline{+\left\{\begin{array}{ccc}\log_x32+\log_y9=7\\\log_x32-\log_y9=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2\log_x32=10\qquad\text{divide both sides by 2}\\.\qquad\log_x32=5\qquad\text{use}\ \log_ab=c\iff a^c=b\\.\qquad x^5=32\to x=\sqrt[5]{32}\to\boxed{x=2}\\\\\text{Substitute}\ \log_x32=5\ \text{to the first equation:}\\5+\log_y9=7\qquad\text{subtract 5 from both sides}[/tex]
[tex]\log_y9=2\qquad\text{use}\ \log_ab=c\iff a^c=b\\y^2=9\to y=\sqrt9\to\boxed{y=3}[/tex]
