The following system of linear equations

$2 x+3 y+2 z=9$......(1)

$3 x+2 y+2 z=9$........(2)

$x-y+4 z=8$........(3)

$(1)-(2) \Rightarrow-x+y=0 \Rightarrow x-y=0$

from (3) $4 \mathrm{z}=8 \Rightarrow \mathrm{z}=2$

from (1) $2 x+3 y=5$

$\Rightarrow x=y=1$

$\therefore$ system has unique solution