Origem: Wikilivros, livros abertos por um mundo aberto.
- Resolva, nos números reais, os sistemas de equações abaixo:
![{\displaystyle \left\{{\begin{matrix}x+y=12\\xy=35\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adaf03752074ba23fd3bc9f26d8acb43bc98317e)
![{\displaystyle \left\{{\begin{matrix}x+y=2\\xy=-2\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee17629fbe8276110c14380ee2ad050e401d25fe)
![{\displaystyle \left\{{\begin{matrix}x-y=7\\xy=30\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c06967f5e66d8f82c6e5976b81da88b5310a5005)
![{\displaystyle \left\{{\begin{matrix}y={\frac {1}{x}}\\x=y+1\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b472b0df1716bf0df632a5c9e8d952e7b725620a)
![{\displaystyle \left\{{\begin{matrix}{\frac {1}{x}}-{\frac {1}{y}}={\frac {1}{6}}\\xy=6\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37c63e13a3b340e38ce4dd638b36d772fd20843e)
![{\displaystyle \left\{{\begin{matrix}x^{2}+y^{2}=25\\x+y=7\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd38c8da7e500a54ed6846135918f5c2eaa0ded3)
![{\displaystyle \left\{{\begin{matrix}x+2y=7\\xy=5\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59c4779ed854e1be16e7e8dc64e4b71d64eac653)
![{\displaystyle \left\{{\begin{matrix}x+y=1\\xy=10\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76ad2bd0970d8904f1d53c6f026ae1c920affba8)
![{\displaystyle \left\{{\begin{matrix}x+2y=3\\xy=1\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7785fafd3695fce30c062aec77e4c806c5282dd5)
![{\displaystyle \left\{{\begin{matrix}x^{2}+y^{2}=13\\x+y=1\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7695fd97582329f2b1d39fd2ad2f124a6609fa3)
![{\displaystyle \left\{{\begin{matrix}x+y=3\\xy=-5\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1907820f3952975c7ee728c3fcbff0f3512e2ea)
![{\displaystyle \left\{{\begin{matrix}x^{2}+y^{2}=26\\x-y=6\end{matrix}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a70b1e15a1123af90a7eb08966292cc12e07188d)
Respostas
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- 1 - (5; 7) e (7; 5).
- 2 - (1 + √3; 1 - √3) e (1 - √3; 1 + √3).
- 3 - (-3; -10) e (10; 3).
- 4 - (0,5 - √1,25; [0,5 - √1,25]-1) e ([0,5 + √1,25]-1; 0,5 + √1,25).
- 5 -
- 6 - (3; 4) e (4; 3).
- 7 - (2; 2,5) e (5; 1).
- 8 - Sem solução.
- 9 - (1; 1) e (2; 0,5).
- 10 - (-2; 3) e (3; -2).
- 11 -
- 12 ´- (5; -1) e (1 e -5).
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