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Solve-the-following-system-of-equations-3x-8z-11-2y-3x-3-y-4z-7-See-the-comment-of-Q-9439-




Question Number 9455 by RasheedSoomro last updated on 09/Dec/16
Solve the following  system of equations  3x−8z=−11  2y−3x=−3  y−4z=−7  See the comment of Q#9439.
$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\mathrm{3x}−\mathrm{8z}=−\mathrm{11} \\ $$$$\mathrm{2y}−\mathrm{3x}=−\mathrm{3} \\ $$$$\mathrm{y}−\mathrm{4z}=−\mathrm{7} \\ $$$${See}\:{the}\:{comment}\:{of}\:{Q}#\mathrm{9439}. \\ $$
Answered by geovane10math last updated on 09/Dec/16
Equation 3: y = 4z − 7  2(4z − 7) − 3x = −3  8z − 14 − 3x = −3  New system:  3x − 8z = −11    (i)  8z − 3x = 11       (ii)     3x − 8z = −11     (i)  −3x + 8z = 11     (ii)  x and z can be any number, because   the equation (i) is only −(ii).
$$\mathrm{Equation}\:\mathrm{3}:\:{y}\:=\:\mathrm{4}{z}\:−\:\mathrm{7} \\ $$$$\mathrm{2}\left(\mathrm{4}{z}\:−\:\mathrm{7}\right)\:−\:\mathrm{3}{x}\:=\:−\mathrm{3} \\ $$$$\mathrm{8}{z}\:−\:\mathrm{14}\:−\:\mathrm{3}{x}\:=\:−\mathrm{3} \\ $$$${New}\:{system}: \\ $$$$\mathrm{3}{x}\:−\:\mathrm{8}{z}\:=\:−\mathrm{11}\:\:\:\:\left({i}\right) \\ $$$$\mathrm{8}{z}\:−\:\mathrm{3}{x}\:=\:\mathrm{11}\:\:\:\:\:\:\:\left({ii}\right)\: \\ $$$$ \\ $$$$\mathrm{3}{x}\:−\:\mathrm{8}{z}\:=\:−\mathrm{11}\:\:\:\:\:\left({i}\right) \\ $$$$−\mathrm{3}{x}\:+\:\mathrm{8}{z}\:=\:\mathrm{11}\:\:\:\:\:\left({ii}\right) \\ $$$${x}\:\mathrm{and}\:{z}\:\mathrm{can}\:\mathrm{be}\:\mathrm{any}\:\mathrm{number},\:\mathrm{because}\: \\ $$$$\mathrm{the}\:\mathrm{equation}\:\left({i}\right)\:\mathrm{is}\:\mathrm{only}\:−\left({ii}\right). \\ $$$$ \\ $$

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