If $x=a,y=b,z=c$is a solution of the system of linear equations $x+8y+7z=0,9x+2y+3z=0,x+y+z=0$such that the point $(a,b,c)$lies on the plane $x+2y+z=6$ then $2a+b+c=$

$a+8b+7c=09a+2b+3c=0,a+b+c=0$

$7b+6c=0,7a+c=0$

$b=\frac{-6c}{7},a=\frac{-c}{7}$

$(a,b,c)$lies on the plane $x+2y+z=6$

$\Rightarrow a+2b+c=6$

$\Rightarrow \frac{-c}{7}-\frac{12c}{7}+c=6$

$\Rightarrow c=-7,b=6,a=1$

$\therefore 2a+b+c=2+6-7=1$