Question

resolva os seguintes sistemas de equação​

Answer 1

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$\tt a)~\begin{cases}\sf2x+2y=6\\\sf x\cdot y=2\end{cases}\\\rm dividindo~a~1^{\underline a}~equac_{\!\!,}\tilde ao~por~2~temos:\\\begin{cases}\sf x+y=3\\\sf x\cdot y=2\end{cases}\\\rm isolando~y~na~1^{\underline a}~equac_{\!\!,}\tilde ao~temos:\\\begin{cases}\sf y=3-x\\\sf x\cdot y=2\end{cases}\\\rm substituindo~y~na~2^{\underline a}~equac_{\!\!,}\tilde ao~teremos:\\\sf x\cdot(3-x)=2\\\sf 3x-x^2=2\\\sf x^2-3x+2=0$

$\sf\Delta=b^2-4ac\\\sf\Delta=(-3)^2-4\cdot1\cdot2\\\sf\Delta=9-8\\\sf\Delta=1\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-3)\pm\sqrt{1}}{2\cdot1}\\\sf x=\dfrac{3\pm1}{2}\begin{cases}\sf x_1=\dfrac{3+1}{2}=\dfrac{4}{2}=2\\\sf x_2=\dfrac{3-1}{2}=\dfrac{2}{2}=1\end{cases}\\\rm substituindo~os~valores~encontrados~na~equac_{\!\!,}\tilde ao~isolada~teremos:\\\sf y=3-x\bigg|_{x=1}=3-1=2\\\sf y=3-x\bigg|_{x=2}=3-2=1\\\rm a~soluc_{\!\!,}\tilde ao~do~sistema~\acute e~dada~por:$

$\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{(1,2),(2,1)\}}}}}\blue{\checkmark}$

$\tt b)~\begin{cases}\sf 4x+y=9\\\sf x+y=14\end{cases}\\\rm vamos~subtrair~a~1^{\underline a}~equac_{\!\!,}\tilde ao~da~2^{\underline a}~equac_{\!\!,}\tilde ao:\\-\underline{\begin{cases}\sf 4x+\diagdown\!\!\!y=9\\\sf x+\diagdown\!\!\!y=14\end{cases}}\\\sf 3x=-5\\\sf x=-\dfrac{3}{5}\\\rm substituindo~x~na~2^{\underline a}~equac_{\!\!,}\tilde ao~teremos:\\\sf -\dfrac{3}{5}+y=14\cdot 5\\\sf -3+5y=70\\\sf 5y=70+3\\\sf 5y=73\\\sf y=\dfrac{73}{5}\\\rm a~soluc_{\!\!,}\tilde ao~do~sistema~\acute e~dada~por:$

$\huge\boxed{\boxed{\boxed{\boxed{\sf S=\bigg\{-\dfrac{3}{5},\dfrac{73}{5}\bigg\}}}}}\blue{\checkmark}$