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[tex]\begin{cases}4x-5y=9\\-5x+2y=-31\end{cases}\\\\\\\begin{cases}4x=9+5y\ \ /:4\\-5x+2y=-31\end{cases}\\\\\\\begin{cases}x=\frac{9}{4}+\frac{5}{4}y\\-5x+2y=-31\end{cases}\\\\\\-5(\frac{9}{4}+\frac{5}{4}y)+2y=-31\\\\-\frac{45}{4}-\frac{25}{4}y+2y=-31\\\\-\frac{25}{4}y+2y=-31+\frac{45}{4}\\\\-\frac{25}{4}y+\frac{8}{4}y=-30\frac{4}{4}+11\frac{1}{4}\\\\-\frac{17}{4}y=-19\frac{3}{4}\\\\-\frac{17}{4}y=-\frac{79}{4}\ \ /:(-\frac{17}{4})\\\\y=\frac{79}{4}:\frac{17}{4}[/tex]
[tex]y=\frac{79}{\not4}\cdot\frac{\not4}{17}\\\\y=\frac{79}{17}\\\\y=4\frac{11}{17}\\\\\\x=\frac{9}{4}+\frac{5}{4}\cdot\frac{79}{17}=\frac{9}{4}+\frac{395}{68}=2\frac{1}{4}+5\frac{55}{68}=2\frac{17}{68}+5\frac{55}{68}=7\frac{72}{68}=8\frac{4}{68}=8\frac{1}{17}\\\\\\\begin{cases}x=8\frac{1}{17}\\y=4\frac{11}{17}\end{cases}[/tex]
[tex]Spr.\\\\\begin{cases}4x-5y=9\ \ /\cdot5\\-5x+2y=-31\ \ /\cdot4\end{cases}\\\\\\+\begin{cases}20x-25y=45\\-20x+8y=-124\end{cases}\\-----------\\-17y=-79\ \ /:(-17)\\\\y=\frac{79}{17}\\\\y=4\frac{11}{17}\\\\\\4x-5\cdot\frac{79}{17}=9\\\\4x-\frac{395}{17}=9\\\\4x=9+\frac{395}{17}\\\\4x=9+23\frac{4}{17}\\\\4x=32\frac{4}{17}\\\\4x=\frac{548}{17}\ \ /:4\\\\x=\frac{\not548^1^3^7}{17}\cdot\frac{1}{\not4_{1}}\\\\x=\frac{137}{17}\\\\x=8\frac{1}{17}[/tex]
[tex]\begin{cases}x=8\frac{1}{17}\\y=4\frac{11}{17}\end{cases}[/tex]
