Задача 68794 Способ подстановкииии...

6380eeadb7391735218c06c8

30.01.2023 18:39:41

Способ подстановкииии

5f3ea7e3faf909182968ddd9

30.01.2023 18:56:05

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a)
[m]\left\{\begin {matrix}10x -10y=1\\6x+y=9\end {matrix}\right.[/m]

[red]Решаем способом подстановки[/red]

[m]\left\{\begin {matrix}10x- 10 \cdot (9-6x)=1\\y=9-6x\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}10x- 90+60x=1\\y=9-6x\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}70x=91\\y=9-6x\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x=1,3\\y=9-6\cdot 1,3\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x=1,3\\y=1,2\end {matrix}\right.[/m]

О т в е т. (1,3;1,2)

б)
[m]\left\{\begin {matrix}12x -4,5y=27\\2x+y=1\end {matrix}\right.[/m]

[red]Решаем способом подстановки[/red]
[m]\left\{\begin {matrix}12x -4,5(1-2x)=27\\y=1-2x\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}12x -4,5+9x=27\\y=1-2x\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}21x =31,5\\y=1-2x\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}x =\frac{63}{2}:21\\y=1-2x\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x =\frac{63}{2}\cdot \frac{1}{21}\\y=1-2x\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x =1,5\\y=1-2\cdot 1, 5\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x =1,5\\y=1-3\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x =1,5\\y=-2\end {matrix}\right.[/m]

О т в е т. (1,5; -2)