Ответ:
Смотри решение на фото..
3) Умножим 2 уравнение на 2 и сложим его с 1 уравнением .
[tex]\left\{\begin{array}{l}3x+5y=4\\4x+3y=-2\ |\cdot 2\end{array}\right\ \oplus \ \left\{\begin{array}{l}3x+5y=4\\11x+11y=0\end{array}\right\ \ \left\{\begin{array}{l}3x-5x=4\\y=-x\end{array}\right\ \ \left\{\begin{array}{l}-2x=4\\y=-x\end{array}\right\\\\\\\left\{\begin{array}{l}x=-2\\y=2\end{array}\right\ \ \ \ Otvet:\ (-2;2)\ .[/tex]
4) Метод подстановки .
[tex]\left\{\begin{array}{l}0,3x+0,5y=2,5\ |\cdot 10\\0,2x+0,4y=1,8\ |\cdot 10\end{array}\right\ \ \left\{\begin{array}{l}3x+5y=25\\2x+4y=18\ |:2\end{array}\right\ \ \left\{\begin{array}{l}3x+5y=25\\x+2y=9\end{array}\right\\\\\\\left\{\begin{array}{l}3(9-2y)+5y=25\\x=9-2y\end{array}\right\ \ \left\{\begin{array}{l}27-6y+5y=25\\x=9-2y\end{array}\right\ \ \left\{\begin{array}{l}y=2\\x=9-2y\end{array}\right[/tex]
[tex]\left\{\begin{array}{l}y=2\\x=9-2\cdot 2\end{array}\right\ \ \left\{\begin{array}{l}y=2\\x=5\end{array}\right\ \ \ \ \Rightarrow \ \ \ Otvet:\ (\, 5\ ;\, 2\ )\ .[/tex]
5) Раскроем скобки, приведём подобные члены и применим метод подстановки .
[tex]\left\{\begin{array}{l}3x-2(x-1)(x+1)-2y=13-2x^2\\6-(y-1)(y+4)=8-2x\end{array}\right\ \ \left\{\begin{array}{l}3x-2(x^2-1)-2y=13-2x^2\\6-(y^2+3y-4)=8-2x\end{array}\right\\\\\\\left\{\begin{array}{l}3x-2y+2=13\\-y^2-3y+10=8-2x\end{array}\right\ \ \left\{\begin{array}{l}3x-2y=11\\y^2+3y-2x=2\end{array}\right[/tex]
[tex]\left\{\begin{array}{l}x=\dfrac{2y+11}{3}\\y^2+3y-2\cdot \dfrac{2y+11}{3}=2\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{2y+11}{3}\\3y^2+9y-4y-22=6\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{2y+11}{3}\\3y^2+5y-28=0\end{array}\right[/tex]
[tex]3y^2+5y-28=0\ \ ,\ \ y_{1,2}=\dfrac{-5\pm \sqrt{25+4\cdot 3\cdot 28}}{6}=\dfrac{-5\pm 19}{6}\ \ ,\\\\y_1=-4\ \ ,\ y_2=\dfrac{7}{3}\\\\\\x_1=\dfrac{-8+11}{3}=1\ \ ,\ \ x_2=\dfrac{\frac{14}{3}+11}{3}=\dfrac{47}{9}\\\\\\Otvet:\ \ \Big(\ 1\ ;-4\ \Big)\ ,\ \Big(\ \dfrac{47}{3}\ ;\ \dfrac{7}{3}\ \Big)\ .[/tex]
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Ответ:
Смотри решение на фото..
Ответ:
3) Умножим 2 уравнение на 2 и сложим его с 1 уравнением .
[tex]\left\{\begin{array}{l}3x+5y=4\\4x+3y=-2\ |\cdot 2\end{array}\right\ \oplus \ \left\{\begin{array}{l}3x+5y=4\\11x+11y=0\end{array}\right\ \ \left\{\begin{array}{l}3x-5x=4\\y=-x\end{array}\right\ \ \left\{\begin{array}{l}-2x=4\\y=-x\end{array}\right\\\\\\\left\{\begin{array}{l}x=-2\\y=2\end{array}\right\ \ \ \ Otvet:\ (-2;2)\ .[/tex]
4) Метод подстановки .
[tex]\left\{\begin{array}{l}0,3x+0,5y=2,5\ |\cdot 10\\0,2x+0,4y=1,8\ |\cdot 10\end{array}\right\ \ \left\{\begin{array}{l}3x+5y=25\\2x+4y=18\ |:2\end{array}\right\ \ \left\{\begin{array}{l}3x+5y=25\\x+2y=9\end{array}\right\\\\\\\left\{\begin{array}{l}3(9-2y)+5y=25\\x=9-2y\end{array}\right\ \ \left\{\begin{array}{l}27-6y+5y=25\\x=9-2y\end{array}\right\ \ \left\{\begin{array}{l}y=2\\x=9-2y\end{array}\right[/tex]
[tex]\left\{\begin{array}{l}y=2\\x=9-2\cdot 2\end{array}\right\ \ \left\{\begin{array}{l}y=2\\x=5\end{array}\right\ \ \ \ \Rightarrow \ \ \ Otvet:\ (\, 5\ ;\, 2\ )\ .[/tex]
5) Раскроем скобки, приведём подобные члены и применим метод подстановки .
[tex]\left\{\begin{array}{l}3x-2(x-1)(x+1)-2y=13-2x^2\\6-(y-1)(y+4)=8-2x\end{array}\right\ \ \left\{\begin{array}{l}3x-2(x^2-1)-2y=13-2x^2\\6-(y^2+3y-4)=8-2x\end{array}\right\\\\\\\left\{\begin{array}{l}3x-2y+2=13\\-y^2-3y+10=8-2x\end{array}\right\ \ \left\{\begin{array}{l}3x-2y=11\\y^2+3y-2x=2\end{array}\right[/tex]
[tex]\left\{\begin{array}{l}x=\dfrac{2y+11}{3}\\y^2+3y-2\cdot \dfrac{2y+11}{3}=2\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{2y+11}{3}\\3y^2+9y-4y-22=6\end{array}\right\ \ \left\{\begin{array}{l}x=\dfrac{2y+11}{3}\\3y^2+5y-28=0\end{array}\right[/tex]
[tex]3y^2+5y-28=0\ \ ,\ \ y_{1,2}=\dfrac{-5\pm \sqrt{25+4\cdot 3\cdot 28}}{6}=\dfrac{-5\pm 19}{6}\ \ ,\\\\y_1=-4\ \ ,\ y_2=\dfrac{7}{3}\\\\\\x_1=\dfrac{-8+11}{3}=1\ \ ,\ \ x_2=\dfrac{\frac{14}{3}+11}{3}=\dfrac{47}{9}\\\\\\Otvet:\ \ \Big(\ 1\ ;-4\ \Big)\ ,\ \Big(\ \dfrac{47}{3}\ ;\ \dfrac{7}{3}\ \Big)\ .[/tex]