Question

4) Qual é a solução da equação (6
13 −2 4) . (x y)= 30 15 ?​

Answer 1

$\large\boxed{\begin{array}{l}\rm Qual\,\acute e\,a\,soluc_{\!\!,}\tilde ao\,da\,equac_{\!\!,}\tilde ao \begin{pmatrix}\sf6&\sf13\\\sf-2&\sf4\end{pmatrix}\cdot\begin{pmatrix}\sf x\\\sf y\end{pmatrix}=\begin{pmatrix}\sf30\\\sf15\end{pmatrix}?\\\underline{\red{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}}\\\sf\begin{pmatrix}\sf6x+13y\\\sf-2x+4y\end{pmatrix}=\begin{pmatrix}\sf30\\\sf15\end{pmatrix}\\\begin{cases}\sf6x+13y=30\\\sf-2x+4y=15\cdot[3]\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}+\underline{\begin{cases}\sf\diagup\!\!\!\!\!6x+13y=30\\\sf-\diagup\!\!\!\!6x+12y=45\end{cases}}\\\sf 25y=75\\\sf y=\dfrac{75}{25}\\\\\sf y=3\\\sf -2x+4y=15\\\sf -2x+4\cdot3=15\\\sf -2x+12=15\\\sf 2x=12-15\\\sf 2x=-3\\\sf x=-\dfrac{3}{2}\\\\\sf S=\bigg\{-\dfrac{3}{2},3\bigg\}\end{array}}$