Question

Qual o par ordenado e solução da equaçao 3x+2y=16

Answer 1

$\boxed{\begin{array}{l}\boldsymbol{Resposta:}~\sf infinitos~pares~ordenados\\\boldsymbol{Explicac_{\!\!,}\tilde ao~passo~a~passo:}\\\sf A~equac_{\!\!,}\tilde ao~3x+2y=16~admite~infinitas~soluc_{\!\!,}\tilde oes\\\sf Contudo~as~soluc_{\!\!,}\tilde oes~triviais~s\tilde ao\\\sf quando~fazemos~x=0~e~encontramos~y\\\sf e~quando~fazemos~y=0~e~encontramos~x.\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm Quando~fazemos~x=0}\\\sf 3\cdot0+2y=16\\\sf 2y=16\\\sf y=\dfrac{16}{2}\\\\\sf y=8\implies o~par~(0,8)~\acute e~soluc_{\!\!,}\tilde ao\\\underline{\rm Quando~fazemos~y=0}\\\sf 3x+2\cdot0=16\\\sf 3x=16\\\sf x=\dfrac{16}{3}\implies o~par~\bigg(\dfrac{16}{3},0\bigg)~\acute e~soluc_{\!\!,}\tilde ao\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm Nota: A~soluc_{\!\!,}\tilde ao~de~uma~equac_{\!\!,}\tilde ao~de~1^o~grau}\\\underline{\rm com~duas~vari\acuter \acute aveis~\acute e~infinita}\\\underline{\rm Por\acute em~O~sistema~composto~por~duas~equac_{\!\!,}\tilde oes~de~1^o~grau}\\\underline{\rm Com~duas~vari\acute aveis~admite~soluc_{\!\!,}\tilde ao~\acute unica.}\end{array}}$