若数$a$使关于$x$的分式方程$\dfrac{x+2}{x-1}+\dfrac{a}{1-x}=3$的解为非负数，且使关于$y$的不等式组\(\begin{cases}\dfrac{y-3}{4}-\dfrac{y+1}{3}\geqslant-\dfrac{7}{6}\\ 2(y-a)