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Question Number 6251 by net last updated on 20/Jun/16

3x−2y−4z=2 3y−4z=−2 2y+6z=−1

$$\mathrm{3}{x}−\mathrm{2}{y}−\mathrm{4}{z}=\mathrm{2} \\ $$$$\mathrm{3}{y}−\mathrm{4}{z}=−\mathrm{2} \\ $$$$\mathrm{2}{y}+\mathrm{6}{z}=−\mathrm{1} \\ $$

Answered by Rasheed Soomro last updated on 20/Jun/16

3x−2y−4z=2.........(i) 3y−4z=−2.............(ii) 2y+6z=−1.............(iii) 2×(ii) : 6y−8z=−4.......(iv) 3×(iii):6y+18z=−3.......(v) (iv)−(v) : −26z=−1⇒z=(1/(26)) Substituting z=(1/(26)) in (ii) 3y−4((1/(26)))=−2⇒3y=−2+(2/(13))=−((24)/(13))⇒y=−((24)/(39)) Substituting values of y and z in (i) 3x−2(−((24)/(39)))−4((1/(26)))=2 3x+((48)/(39))−(2/(13))=2⇒117x+48−6=78 x=((78−42)/(117))=((36)/(117))=(4/(13))⇒x=(4/(13))

$$\mathrm{3}{x}−\mathrm{2}{y}−\mathrm{4}{z}=\mathrm{2}.........\left({i}\right) \\ $$$$\mathrm{3}{y}−\mathrm{4}{z}=−\mathrm{2}.............\left({ii}\right) \\ $$$$\mathrm{2}{y}+\mathrm{6}{z}=−\mathrm{1}.............\left({iii}\right) \\ $$$$ \\ $$$$\mathrm{2}×\left({ii}\right)\::\:\mathrm{6}{y}−\mathrm{8}{z}=−\mathrm{4}.......\left({iv}\right) \\ $$$$\mathrm{3}×\left({iii}\right):\mathrm{6}{y}+\mathrm{18}{z}=−\mathrm{3}.......\left({v}\right) \\ $$$$\left({iv}\right)−\left({v}\right)\::\:−\mathrm{26}{z}=−\mathrm{1}\Rightarrow{z}=\frac{\mathrm{1}}{\mathrm{26}} \\ $$$${Substituting}\:{z}=\frac{\mathrm{1}}{\mathrm{26}}\:\:{in}\:\:\left({ii}\right) \\ $$$$\mathrm{3}{y}−\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{26}}\right)=−\mathrm{2}\Rightarrow\mathrm{3}{y}=−\mathrm{2}+\frac{\mathrm{2}}{\mathrm{13}}=−\frac{\mathrm{24}}{\mathrm{13}}\Rightarrow{y}=−\frac{\mathrm{24}}{\mathrm{39}} \\ $$$${Substituting}\:{values}\:{of}\:{y}\:{and}\:{z}\:{in}\:\:\left({i}\right) \\ $$$$\mathrm{3}{x}−\mathrm{2}\left(−\frac{\mathrm{24}}{\mathrm{39}}\right)−\mathrm{4}\left(\frac{\mathrm{1}}{\mathrm{26}}\right)=\mathrm{2} \\ $$$$\mathrm{3}{x}+\frac{\mathrm{48}}{\mathrm{39}}−\frac{\mathrm{2}}{\mathrm{13}}=\mathrm{2}\Rightarrow\mathrm{117}{x}+\mathrm{48}−\mathrm{6}=\mathrm{78} \\ $$$${x}=\frac{\mathrm{78}−\mathrm{42}}{\mathrm{117}}=\frac{\mathrm{36}}{\mathrm{117}}=\frac{\mathrm{4}}{\mathrm{13}}\Rightarrow{x}=\frac{\mathrm{4}}{\mathrm{13}} \\ $$

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