The system of equations x + y + z = 9, 2x + 5y + 7z = 52, 2x + y - z = 0 are consistent and
have unique solution (x, y, z) then $x-y+z=$__________

$$\begin{gathered} \begin{array}{l}\mathrm{AD}=\left[\begin{array}{llll}1& 1& 1& 9\\ 2& 5& 7& 52\\ 2& 1& -1& 0\end{array}\right],\mathrm{A}=\left[\begin{array}{ccc}1& 1& 1\\ 2& 5& 7\\ 2& 1& -1\end{array}\right]\\ {\mathrm{R}}_2\to {\mathrm{R}}_2-2{\mathrm{R}}_1, {\mathrm{R}}_3\to {\mathrm{R}}_3-2{\mathrm{R}}_1 \\ \left[\begin{array}{cccc}1& 1& 1& 9\\ 0& 3& 5& 34\\ 0& -1& -3& -18\end{array}\right]\\ {\mathrm{R}}_3\to 3{\mathrm{R}}_3+{\mathrm{R}}_2\left[\begin{array}{cccc}1& 1& 1& 9\\ 0& 3& 5& 34\\ 0& 0& -4& -20\end{array}\right]\end{array} \end{gathered}$$
Rank A=3, Rank(AD) =3, unknown variables =3
Costs tent and it has unsure solution
x+ y+ z=9
3y + 5z= 34
-4z =-20$\Rightarrow$z=5
3y+25=34$\Rightarrow$3y=9$\Rightarrow$y=3
x+3+5=9$\Rightarrow$x=1
x-y+z=5-3+1=3