Wyznaczmy współrzędne punktów przecięcia się prostych.

$\{\begin{array}{l}y=3x-6\\ y=\frac{1}{3}x+2\end{array}$  

 

$\{\begin{array}{l}y=3x-6\\ 3x-6=\frac{1}{3}x+2\mid \cdot 3\end{array}$  

 

$\{\begin{array}{l}y=3x-6\\ 9x-18=x+6\end{array}$  

 

$\{\begin{array}{l}y=3x-6\\ 8x=24\end{array}$  

 

$\{\begin{array}{l}y=3\cdot 3-6\\ x=3\end{array}$  

 

$\{\begin{array}{l}y=3\\ x=3\end{array}$   

 

---

$\{\begin{array}{l}y=3x-6\\ y=-x+2\end{array}$  

$\{\begin{array}{l}-x+2=3x-6\\ y=-x+2\end{array}$  

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

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

$\{\begin{array}{l}x=2\\ y=0\end{array}$  

 

---

$\{\begin{array}{l}y=\frac{1}{3}x+2\\ y=-x+2\end{array}$  

$\{\begin{array}{l}-x+2=\frac{1}{3}x+2\mid \cdot 3\\ y=-x+2\end{array}$  

$\{\begin{array}{l}-3x+6=x+6\\ y=-x+2\end{array}$  

$\{\begin{array}{l}-4x=0\\ y=-x+2\end{array}$  

$\{\begin{array}{l}x=0\\ y=2\end{array}$  

 

Odp.:

a)

Proste     $y=3x-6$   oraz  $y=-x+2$  

 

b)

Proste  $y=\frac{1}{3}x+2$   oraz  $y=-x+2$