Решите пожалуйста систему уравнений! [tex]\left \{ {{-5x+4y=-2} \atop {3x+7y=-27}} \right.[/tex]. Created by qepardios. algebra-ru

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$\left \{ {{x=\frac{2}{5}+\frac{4}{5}y } \atop {3x+7y=-27}} \right. \\\\\\3(\frac{2}{5}+\frac{4}{5}y)+7y=-27\\\\\frac{6}{5}+\frac{12}{5}y+7y=-27 \\\\6+47y=-135\\47y=-141\\y=-3\\\\\\x=-2\\\\\\(x;y)=(-2;-3)$

Объяснение:

Надеюсь понятно

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$\displaystyle\begin{cases}-5x+4y=-2,\\3x+7y=-27;\end{cases}\Longleftrightarrow\begin{cases}4y=-2+5x,\\3x+7y=-27;\end{cases}\Longleftrightarrow\begin{cases}y=-\dfrac{1}{2}+\dfrac54x\\3x+7(-\dfrac12+\dfrac54x)=-27\end{cases}$ $\displaystyle3x+7\Big(-\frac12+\frac54x\Big)=-27\\\\3x-\frac72+\frac{35}4x=-27$

$3x-3.5+8.75x=-27\\11.75x-3.5=-27\\11.75x=-27+3.5\\11.75x=-23.5\\\\x=-\dfrac{23.5}{11.75}\\\\x=-2\\\\\\y=-\dfrac12+\dfrac54x\\\\y=-\dfrac12+\dfrac54(-2)\\\\y=-0.5-2.5\\y=-3$

Ответ: (-2; -3)

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