Question

Elabore e resolva um problema envolvendo equações lineares simultâneas, no qual possa ser empregado o uso de técnicas algébricas de resolução:

Answer 1

$\large\boxed{\begin{array}{l}\rm Num~terreno~h\acute a~c\tilde aes~e~galinhas~num~total\\\rm de~14~animais~e~36~p\acute es. Quantas~animais~de~cada~tipo\\\rm h\acute a~nesse~terreno?\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf c\longrightarrow n^o~de~c\tilde aes\\\sf g\longrightarrow n^o~de~galinhas\\\begin{cases}\sf c+g=14\\\sf 4c+2g=36\end{cases}\\\underline{\rm isole~g~na~1^a~equac_{\!\!,}\tilde ao:}\\\begin{cases}\sf g=14-c\\\sf 4c+2g=36\end{cases}\\\underline{\rm substitua~na~2^a~equac_{\!\!,}\tilde ao:}\\\sf 4c+2\cdot(14-c)=36\\\sf 4c+28-2c=36\\\sf 4c-2c=36-28\\\sf 2c=8\\\sf c=\dfrac{8}{2}\\\sf c=4\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm substitua~ c~na~equac_{\!\!,}\tilde ao}\\\underline{\rm com~vari\acute avel~isolada:}\\\sf g=14-c\\\sf g=14-4\\\sf g=10\\\rm Neste~terreno~h\acute a~4~c\tilde aes~e~10~galinhas\end{array}}$