$\begin{array} { l }\frac{ 10 }{ y }=\frac{ 11 }{ 8 },& y≠0\end{array}$
Simplify the equation using cross-multiplication$80=11y$
Swap the sides of the equation$11y=80$
Divide both sides of the equation by $11$$\begin{array} { l }y=\frac{ 80 }{ 11 },& y≠0\end{array}$
Check if the solution is in the defined range$\begin{align*}&y=\frac{ 80 }{ 11 } \\&\begin{array} { l }y=7 \frac{ 3 }{ 11 },& y=7.\overset{ \cdot }{ 2 } \overset{ \cdot }{ 7 } \end{array}\end{align*}$