Resolva o sistema LINEAR abaixo pelo método que preferir {-x-y=-6 2x-3y=-3
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Boa noite!
Solução!
Vou resolver pelo método da adição,podendo ser resolvido por outros métodos.
![\begin{cases}
-x-y=-6\\
2x-3y=-3
\end{cases}\\\\\\\\\
Vamos~~multplicar~~ a~~ primeira~~ equacao~~por -3\\\\\\\
\begin{cases}
-x-y=-6.(-3)\\
2x-3y=-3
\end{cases}\\\\\\\\\
\begin{cases}
-x-y=-6.(-3)\\
2x-3y=-3
\end{cases}\\\\\\\\\](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%0A-x-y%3D-6%5C%5C%0A2x-3y%3D-3%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AVamos%7E%7Emultplicar%7E%7E+a%7E%7E+primeira%7E%7E+equacao%7E%7Epor+-3%5C%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0A-x-y%3D-6.%28-3%29%5C%5C%0A2x-3y%3D-3%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cbegin%7Bcases%7D%0A-x-y%3D-6.%28-3%29%5C%5C%0A2x-3y%3D-3%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A%0A%0A%0A%0A%0A "\begin{cases}
-x-y=-6\\
2x-3y=-3
\end{cases}\\\\\\\\\
Vamos~~multplicar~~ a~~ primeira~~ equacao~~por -3\\\\\\\
\begin{cases}
-x-y=-6.(-3)\\
2x-3y=-3
\end{cases}\\\\\\\\\
\begin{cases}
-x-y=-6.(-3)\\
2x-3y=-3
\end{cases}\\\\\\\\\")
![\begin{cases}
3x+3y=18\\
2x-3y=-3
\end{cases}\\\\\\\\\
Veja: ~~anulou~~ a~~variavel ~~y\\\\\\
3x+2x=18-3\\\\\
5x=15\\\\\
x= \dfrac{15}{5}\\\\\
x=3](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%0A3x%2B3y%3D18%5C%5C%0A2x-3y%3D-3%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AVeja%3A+%7E%7Eanulou%7E%7E+a%7E%7Evariavel+%7E%7Ey%5C%5C%5C%5C%5C%5C%0A3x%2B2x%3D18-3%5C%5C%5C%5C%5C%0A5x%3D15%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B15%7D%7B5%7D%5C%5C%5C%5C%5C%0Ax%3D3+%0A%0A%0A "\begin{cases}
3x+3y=18\\
2x-3y=-3
\end{cases}\\\\\\\\\
Veja: ~~anulou~~ a~~variavel ~~y\\\\\\
3x+2x=18-3\\\\\
5x=15\\\\\
x= \dfrac{15}{5}\\\\\
x=3")
Vamos agora determinar o valor de y fazendo a substituição!
![2x-3y=-3 \\\\\\
2(3)-3y=-3\\\\\
6-3y=-3\\\\\
-3y=-3-6\\\\\
3y=-9\\\\\
y=\dfrac{-9}{3}\\\\\
y=-3\\\\\\\\\\
\boxed{Resposta:x=3~~y=-3}](https://tex.z-dn.net/?f=2x-3y%3D-3+%5C%5C%5C%5C%5C%5C%0A2%283%29-3y%3D-3%5C%5C%5C%5C%5C%0A6-3y%3D-3%5C%5C%5C%5C%5C%0A-3y%3D-3-6%5C%5C%5C%5C%5C%0A3y%3D-9%5C%5C%5C%5C%5C%0Ay%3D%5Cdfrac%7B-9%7D%7B3%7D%5C%5C%5C%5C%5C%0Ay%3D-3%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3Ax%3D3%7E%7Ey%3D-3%7D+ "2x-3y=-3 \\\\\\
2(3)-3y=-3\\\\\
6-3y=-3\\\\\
-3y=-3-6\\\\\
3y=-9\\\\\
y=\dfrac{-9}{3}\\\\\
y=-3\\\\\\\\\\
\boxed{Resposta:x=3~~y=-3}")
Boa noite!
Bons estudos!
Solução!
Vou resolver pelo método da adição,podendo ser resolvido por outros métodos.
Vamos agora determinar o valor de y fazendo a substituição!
Boa noite!
Bons estudos!
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