\(x\left(y+3\right)-7y=11\Leftrightarrow x\left(y+3\right)-7\left(y+3\right)=11-21=-10\)
\(\left(y+3\right)\left(x-7\right)=-10\)
\(\hept{\begin{cases}y+3=\left(-10,-5,-2,-1,1,2,5,10\right)\\x-10=\left(1,2,5,10,-10,-5,-2,-1\right)\end{cases}}\)\(\hept{\begin{cases}y=\left\{-13,-8,-5,-4,-2,-1,2,7\right\}\\x=\left\{11,12,15,20,0,5,8,9\right\}\end{cases}}\)