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Question Number 151028 by kalenis last updated on 17/Aug/21

Answered by amin96 last updated on 17/Aug/21

 { ((x+y−z=7     −)),((x−y+2z=3)),((2x+y+z=9)) :}⇒ { ((2x+z=10)),((10+y=9)) :} ⇒ { ((2x+z=10)),((y=−1)) :}   { ((x−z=8)),((x+2z=2)) :}   { ((2x−2z=16)),((x+2z=2)) :}⇒3x=18  x=6  x−z=8  ⇒  z=−2     answer  (6;  −1;  −2)

$$\begin{cases}{{x}+{y}−{z}=\mathrm{7}\:\:\:\:\:−}\\{{x}−{y}+\mathrm{2}{z}=\mathrm{3}}\\{\mathrm{2}{x}+{y}+{z}=\mathrm{9}}\end{cases}\Rightarrow\begin{cases}{\mathrm{2}{x}+{z}=\mathrm{10}}\\{\mathrm{10}+{y}=\mathrm{9}}\end{cases}\:\Rightarrow\begin{cases}{\mathrm{2}{x}+{z}=\mathrm{10}}\\{{y}=−\mathrm{1}}\end{cases} \\ $$$$\begin{cases}{{x}−{z}=\mathrm{8}}\\{{x}+\mathrm{2}{z}=\mathrm{2}}\end{cases}\:\:\begin{cases}{\mathrm{2}{x}−\mathrm{2}{z}=\mathrm{16}}\\{{x}+\mathrm{2}{z}=\mathrm{2}}\end{cases}\Rightarrow\mathrm{3}{x}=\mathrm{18}\:\:{x}=\mathrm{6} \\ $$$${x}−{z}=\mathrm{8}\:\:\Rightarrow\:\:{z}=−\mathrm{2}\:\:\:\:\:{answer}\:\:\left(\mathrm{6};\:\:−\mathrm{1};\:\:−\mathrm{2}\right) \\ $$

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