$\text{a)}$  

$\{\begin{array}{l}2x+y+z=8\mid \cdot \left(-2\right)\\ x-y+2z=7\end{array}$  

$\{\begin{array}{l}-4x-2y-2z=-16\\ x-y+2z=7\end{array}$  

Dodajemy do siebie lewe i prawe strony równań.

$+\{\begin{array}{l}-4x-2y-2z=-16\\ x-y+2z=7\end{array}$  
____________________

$-3x-3y=-9\mid \cdot \left(-1\right)$  

$3x+3y=9$  

$3\left(x+y\right)=9\mid :3$  

$x+y=3$  

---

$\text{b)}$  

$\{\begin{array}{l}2x+y+z=8\\ x-y+2z=7\end{array}$  

Dodajemy do siebie lewe i prawe strony równań.

$\{\begin{array}{l}2x+y+z=8\\ x-y+2z=7\end{array}$  
____________________

$3x+3z=15\mid \cdot \left(-1\right)$  

$3\left(x+z\right)=15\mid :3$  

$x+z=5$  

---

$\text{c)}$  

$\{\begin{array}{l}2x+y+z=8\\ x-y+2z=7\mid \cdot \left(-2\right)\end{array}$  

$\{\begin{array}{l}2x+y+z=8\\ -2x+2y-4z=-14\end{array}$  

Dodajemy do siebie lewe i prawe strony równań.

$+\{\begin{array}{l}2x+y+z=8\\ -2x+2y-4z=-14\end{array}$  
____________________

$3y-3z=-6$  

$3\left(y-z\right)=-6\mid :3$  

$y-z=-2$