Question

solucione os sistemas a seguir 2a+b+c=-1
a+c=0
-3a+5b-c=2​

Answer 1

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$\large\green{\boxed{\rm~~~\orange{a}~\pink{=}~\blue{ -1}~\green{,}~\orange{b}~\pink{=}~\blue{ 1}~\green{e}~\orange{c}~\pink{=}~\blue{ 0 }~~~}}$

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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☺lá, Msk, como tens passado nestes tempos de quarentena⁉ E os estudos à distância, como vão⁉ Espero que bem❗ Acompanhe a resolução abaixo, feita através de algumas manipulações algébricas, e após o resultado você encontrará um link com mais informações sobre Resolução de Sistemas por Matrizes que talvez te ajude com exercícios semelhantes no futuro. ✌

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$\large\gray{\boxed{\rm\blue{ I)~2a + b + c = -1 }}}$

$\large\gray{\boxed{\rm\blue{ II)~a + c = 0 }}}$

$\large\gray{\boxed{\rm\blue{ III)~-3a + 5b - c = 2 }}}$

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☔ De II) temos

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➡ $\sf\large\blue{ a = -c }$

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☔ De II) temos em III) temos

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➡ $\sf\large\blue{ -3 \cdot (-c) + 5b - c = 2 }$

➡ $\sf\large\blue{ 3c + 5b - c = 2 }$

➡ $\sf\large\blue{ 2c = 2 - 5b }$

➡ $\sf\large\blue{ c = \dfrac{2 - 5b}{2} }$

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☔ De II) e III) em I) temos

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➡ $\sf\large\blue{2 \cdot \dfrac{-(2 - 5b)}{2} +b + \dfrac{2 - 5b}{2} = -1 }$

➡ $\sf\large\blue{-2 \cdot \dfrac{2 - 5b}{2} + \dfrac{2b}{2} + \dfrac{2 - 5b}{2} = -1 }$

➡ $\sf\large\blue{-4 + 10b + 2b + 2 - 5b = -2 }$

➡ $\sf\large\blue{7b = 0 }$

➡ $\sf\large\blue{b = 0 }$

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➡ $\sf\large\blue{ c = \dfrac{2 - 0}{2} }$

➡ $\sf\large\blue{ c = 1 }$

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➡ $\sf\large\blue{ a = -1 }$

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$\large\green{\boxed{\rm~~~\orange{a}~\pink{=}~\blue{ -1}~\green{,}~\orange{b}~\pink{=}~\blue{ 1 }~\green{e}~\orange{c}~\pink{=}~\blue{ 0 }~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

✈ Método de Cramer para sistemas (https://brainly.com.br/tarefa/36041850)

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\large\textit{"Absque~sudore~et~labore}$

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