Question

resolva os sistemas usando o metodo do escalonamento

Answer 1

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$\boxed{\begin{array}{l}\begin{cases}\sf 2x-3y-2z=-3\\\sf x+2y+3z=2\\\sf-4x+2y+3z=1\end{cases}\\\underline{\sf permutando~a~2^{a}~equac_{\!\!,}\tilde ao~com~a~1^{a}\!:}\\\begin{cases}\sf x+2y+3z=2\\\sf 2x-3y-2z=-3\\\sf -4x+2y+3z=1\end{cases}\\\underline{\sf multiplicando~a~1^{a} equac_{\!\!,}\tilde ao~por~-2~e~somando~a~2^{a}~e~}\\\underline{\sf em~seguida~multiplicando~a~1^{a} equac_{\!\!,}\tilde ao}\\\underline{\sf~por~4~e~somando~a~3^{a}~temos:}\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf x+2y+3z=2\\\sf-7y-8z=-7\\\sf10y+15z=9\end{cases}\\\underline{\sf multiplicando~a~2^{a} equac_{\!\!,}\tilde ao~por~10~e~a~3^{a}~equac_{\!\!,}\tilde ao}\\\underline{\sf por~7~temos\!:}\\\begin{cases}\sf x+2y+3z=2\\\sf-70y-80z=-70\\\sf70y+105z=63\end{cases}\\\underline{\sf somando~a~2^{a}~equac_{\!\!,}\tilde ao~com~a~3^{a}~temos\!:}\\\begin{cases}\sf x+2y+3z=2\\\sf-70y-80z=-70\\\sf25z=-7\end{cases}\\\sf 25z=-7\\\sf z=\dfrac{-7}{25}\\\sf -70y-80z=-70\div(-10)\end{array}}$

$\large\boxed{\begin{array}{l}\sf 7y-8z=7\\\sf7y-8\cdot\bigg(\!\!-\!\dfrac{7}{25}\bigg )=7\cdot25\\\sf 7y+56=175\\\sf 7y=175-56\\\sf 7y=119\\\sf y=\dfrac{119}{7}\\\sf y=17\\\sf x+2y+3z=2\\\sf x+2\cdot17+3\cdot\bigg(-\dfrac{7}{25}\bigg)=2\cdot25\\\sf 25x+850-21=50\\\sf 25x=50+21-850\\\sf 25x=-779\\\sf x=\dfrac{-779}{25}\\\\\sf S=\bigg\{-\dfrac{779}{25},17,-\dfrac{7}{25}\bigg\}\end{array}}$