Odpowiedź:
[tex]Zad.1\\\\a)\\\\+\begin{cases}x-y=2\\2x+y=13\end{cases}\\--------\\3x=15\ \ /:3\\x=5\\\\\\5-y=2\\\\-y=2-5\\\\-y=-3\ \ /\cdot(-1)\\\\y=3\\\\\\\begin{cases}x=5\\y=3\end{cases}[/tex]
[tex]b)\\\\\begin{cases}3x-4y=15\\7x+2y=1\ \ /\cdot2\end{cases}\\\\\\+\begin{cases}3x-4y=15\\14x+4y=2\end{cases}\\--------\\17x=17\ \ /:17\\x=1\\\\\\7\cdot1+2y=1\\\\7+2y=1\\\\2y=1-7\\\\2y=-6\ \ /:2\\\\y=-3\\\\\\\begin{cases}x=1\\y=-3\end{cases}[/tex]
[tex]c)\\\\\begin{cases}-2x+3y=5\ \ /\cdot3\\6x-8y=3\end{cases}\\\\\\+\begin{cases}-6x+9y=15\\6x-8y=3\end{cases}\\---------\\y=18\\\\\\-2x+3\cdot18=5\\\\-2x+54=5\\\\-2x=5-54\\\\-2x=-49\ \ /:(-2)\\\\x=-\frac{49}{2}\\\\x=-24,5\\\\\\\begin{cases}x=-24,5\\y=18\end{cases}[/tex]
[tex]d)\\\\\begin{cases}3x-5y=3,5\\-4x+2y=-7\end{cases}\\\\\\+\begin{cases}12x-20y=14\\-12x+6y=-21\end{cases}\\----------\\-14y=-7\ \ /:(-14)\\\\y=\frac{7}{14}\\\\y=\frac{1}{2}\\\\\\-4x+\not2\cdot\frac{1}{\not2}=-7\\\\-4x+1=-7\\\\-4x=-7-1\\\\-4x=-8\ \ /:(-4)\\\\x=2\\\\\\\begin{cases}x=2\\y=\frac{1}{2}\end{cases}[/tex]
[tex]e)\\\\\begin{cases}2x+3y=15\\2(2x+3y)=30\end{cases}\\\\\\\begin{cases}2x+3y=15\\4x+6y=30\ \ /:(-2)\end{cases}\\\\\\+\begin{cases}2x+3y=15\\-2x-3y=-15\end{cases}\\----------\\0=0\\\\Uklad\ \ r\'owna\'n\ \ nieoznaczony\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n[/tex]
[tex]f)\\\\\begin{cases}2(x+y)=2-2y\\x+2y=6\end{cases}\\\\\\\begin{cases}2x+2y+2y=2\\x+2y=6\end{cases}\\\\\\\begin{cases}2x+4y=2\ \ /:(-2)\\x+2y=6\end{cases}\\\\\\+\begin{cases}-x-2y=-1\\x+2y=6\end{cases}\\---------\\0=5\\\\Uklad\ \ r\'owna\'n\ \ sprzeczny\ \ nie\ \ ma\ \ rozwiazania[/tex]
