Question

O conjunto solução do sistema abaixo é:

a) S={(1,2)}
b) S = {(2,1)}
c) S = {(2,2)}
d )S = {(1,1)}

Answer 1

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$\begin{cases}\sf5x-3y=2\\\sf\dfrac{x}{2}+\dfrac{y}{3}=\dfrac{5}{6}\end{cases}\\\underline{\rm multiplicando~a~2^{\underline a}~equac_{\!\!,}\tilde ao~por~6~temos:}\\\begin{cases}\sf5x-3y=2\\\sf3x+2y=5\end{cases}\\\underline{\rm multiplicando~a~1^{\underline a}~equac_{\!\!,}\tilde ao~por~2~e~a~2^{\underline a}~equac_{\!\!,}\tilde ao~por~3~temos:}$

$\begin{cases}\sf10x-6y=4\\\sf9x+6y=15\end{cases}\\\underline{\rm vamos~somar~algebricamente~as~duas~equac_{\!\!,}\tilde oes:}\\+\underline{\begin{cases}\sf10x-\diagdown\!\!\!\!\!\!6y=4\\\sf9x+\diagdown\!\!\!\!\!\!6y=15\end{cases}}\\\sf 19x=19\\\sf x=\dfrac{19}{19}\\\sf x=1\\\underline{\rm substituindo~x~na~1^{\underline a}~equac_{\!\!,}\tilde ao~temos:}\\\sf5x-3y=2\\\sf 5\cdot1-3y=2\\\sf 5-3y=2\\\sf 3y=5-2\\\sf 3y=3\\\sf y=\dfrac{3}{3}\\\sf y=1$

$\underline{\sf o~conjunto~soluc_{\!\!,}\tilde ao~\acute e:}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{1,1\}}}}}\blue{\checkmark}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~d}}}}$