$8x+11y=9\Rightarrow 11y\overset{8}{\mathop{\equiv }}\,9\Rightarrow 3y\overset{8}{\mathop{\equiv }}\,\xrightarrow[\left( 8,3 \right)=1]{\div 3}y\overset{8}{\mathop{\equiv }}\,3\Rightarrow y=8k+3$  $y\langle 100\Rightarrow 8k+3\langle 100\Rightarrow k\le 12\Rightarrow {{y}_{\max }}=8\times 12+3=99\Rightarrow 9+9=18$