Question

gente pfvr eu imploro me ajudem​

Answer 1

Resposta:

OLÁ VAMOS A SUA PERGUNTA:⇒⇒

$\left. \begin{cases} { 4x+5y=105 } \\ { 5x+7y=138 } \end{cases} \right.$

$4x+5y=105,5x+7y=138$

$\left(\begin{matrix}4&5\\5&7\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}105\\138\end{matrix}\right)$

$inverse(\left(\begin{matrix}4&5\\5&7\end{matrix}\right))\left(\begin{matrix}4&5\\5&7\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&5\\5&7\end{matrix}\right))\left(\begin{matrix}105\\138\end{matrix}\right)$

$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&5\\5&7\end{matrix}\right))\left(\begin{matrix}105\\138\end{matrix}\right)$

$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}4&5\\5&7\end{matrix}\right))\left(\begin{matrix}105\\138\end{matrix}\right)$

$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{7}{4\times 7-5\times 5}&-\frac{5}{4\times 7-5\times 5}\\-\frac{5}{4\times 7-5\times 5}&\frac{4}{4\times 7-5\times 5}\end{matrix}\right)\left(\begin{matrix}105\\138\end{matrix}\right)$

$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{7}{3}&-\frac{5}{3}\\-\frac{5}{3}&\frac{4}{3}\end{matrix}\right)\left(\begin{matrix}105\\138\end{matrix}\right)$

$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{7}{3}\times 105-\frac{5}{3}\times 138\\-\frac{5}{3}\times 105+\frac{4}{3}\times 138\end{matrix}\right)$

$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}15\\9\end{matrix}\right)$

$\star \: \text{Extraia os elementos x e y da matriz.}$

$\color{blue}{}\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese  x=15,y=9 }}}\ \checkmark$

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$\color{blue}{}\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese b }}}\ \checkmark$

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