Odpowiedź:
[tex]a)\\\\\begin{cases}5x+2y=1\\10x+4y=2\end{cases}\\\\\\\begin{cases}5x=1-2y\ \ /:5\\10x+4y=2\end{cases}\\\\\\\begin{cases}x=\frac{1}{5}-\frac{2}{5}y\\10x+4y=2\end{cases}\\\\\\10(\frac{1}{5}-\frac{2}{5}y)+4y=2\\\\2-4y+4y=2\\\\2=2\\\\Uklad\ \ r\'owna\'n\ \ nieoznaczony\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n[/tex]
[tex]b)\\\\\begin{cases}5x+2y=1\\10x-4y=2\end{cases}\\\\\\\begin{cases}5x=1-2y\ \ /:5\\10x-4y=2\end{cases}\\\\\\\begin{cases}x=\frac{1}{5}-\frac{2}{5}y\\10x-4y=2\end{cases}\\\\\\10(\frac{1}{5}-\frac{2}{5}y)-4y=2\\\\2-4y-4y=2\\\\-8y=2-2\\\\-8y=0\ \ /:(-8)\\\\y=0\\\\x=\frac{1}{5}-\frac{2}{5}\cdot0\\\\x=\frac{1}{5}\\\\\begin{cases}x=\frac{1}{5}\\y=0\end{cases}[/tex]
[tex]c)\\\\\begin{cases}x+y=5\ \ /\cdot(-1)\\2x+y=3\end{cases}\\\\\\+\begin{cases}-x-y=-5\\2x+y=3\end{cases}\\---------\\x=-2\\\\\\-2+y=5\\\\y=5+2\\\\y=7\\\\\begin{cases}x=-2\\y=7\end{cases}[/tex]
