Q.Using Cramer's Rule, solve the system $x+y+z=9$, $2x-y+z=5$, $x+2y-z=4$.

$\Delta=\begin{vmatrix}1&1&1\\2&-1&1\\1&2&-1\end{vmatrix}=1(1-2)-1(-2-1)+1(4+1)=-1+3+5=7$

$\Delta_x=\begin{vmatrix}9&1&1\\5&-1&1\\4&2&-1\end{vmatrix}=9(1-2)-1(-5-4)+1(10+4)=-9+9+14=14$

$\Delta_y=\begin{vmatrix}1&9&1\\2&5&1\\1&4&-1\end{vmatrix}=1(-5-4)-9(-2-1)+1(8-5)=-9+27+3=21$

$\Delta_z=\begin{vmatrix}1&1&9\\2&-1&5\\1&2&4\end{vmatrix}=1(-4-10)-1(8-5)+9(4+1)=-14-3+45=28$