Question Number 115023 by bobhans last updated on 23/Sep/20
$${solve}\:\begin{cases}{\mathrm{7}{x}−\mathrm{5}{y}+\mathrm{3}{z}=\mathrm{6}}\\{\mathrm{2}{x}+\mathrm{4}{y}−\mathrm{5}{z}=−\mathrm{5}}\\{\mathrm{9}{x}−\mathrm{8}{y}+\mathrm{2}{z}=−\mathrm{1}}\end{cases}.\:{Find}\:{x}+{y}+{z}\: \\ $$
Answered by bemath last updated on 23/Sep/20
Answered by PRITHWISH SEN 2 last updated on 23/Sep/20
$$\mathrm{adding}\:\mathrm{all}\:\mathrm{three}\:\mathrm{equations} \\ $$$$\mathrm{18x}−\mathrm{9y}=\mathrm{0}\Rightarrow\mathrm{2x}=\mathrm{y} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{two}\:\mathrm{equations}\:\mathrm{will}\:\mathrm{be} \\ $$$$\:\:\mathrm{x}−\mathrm{z}=−\mathrm{2} \\ $$$$\:\:\mathrm{2x}−\mathrm{z}=−\mathrm{1} \\ $$$$\mathrm{solving}\:\mathrm{x}=\mathrm{1}\:\mathrm{y}=\mathrm{2}\:\mathrm{z}=\:\mathrm{3} \\ $$$$\therefore\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}=\mathrm{6} \\ $$