[tex]\it Notez\ numerele\ cerute\ cu\ x,\ y,\ z.\\ \\ x>y\ cu\ 6 \Rightarrow x=z+6\ \ \ \ (1)\\ \\ x-y=y-z \Rightarrow x+z=y+y \Rightarrow x+z=2y \Rightarrow 2y=x+z \stackrel{(1)}{\Longrightarrow} \ 2y=z+6+z \Rightarrow\\ \\ \Rightarrow2y=2z+6|_{:2} \Rightarrow y=z+3\ \ \ \ \ (2)[/tex]
[tex]\it x+y+z=42\ \stackrel{(1),(2)}{\Longrightarrow}\ \ z+6+z+3+z=42 \Rightarrow3z+9=42|_{:3} \Rightarrow\\ \\ \Rightarrow z+3=14 \Rightarrow z=14-3 \Rightarrow z=11\ \ \ \ (3) \\ \\ (1),\ (3) \Rightarrow x=11+6 \Rightarrow x=17\\ \\ (2),\ (3) \Rightarrow y=11+3 \Rightarrow y=14\\ \\ Numerele\ cerute\ sunt\ :x=17,\ y=14,\ z=11[/tex]
