Odpowiedź:
[tex]a)\\\\\begin{cases}3x-2y=-4\\x+y=-3\ \ /\cdot2\end{cases}\\\\\\+\begin{cases}3x-2y=-4\\2x+2y=-6\end{cases}\\---------\\5x=-10\ \ /:5\\x=-2\\\\\\-2+y=-3\\\\y=-3+2\\\\y=-1\\\\\begin{cases}x=-2\\y=-1\end{cases}[/tex]
[tex]b)\\\\\begin{cases}2x-3y=-4\ \ /\cdot(-2)\\3x-2y=-1\ \ /\cdot3\end{cases}\\\\\\+\begin{cases}-4x+6y=8\\9x-6y=-3\end{cases}\\---------\\5x=5\ \ /:5\\x=1\\\\\\3\cdot1-2y=-1\\\\3-2y=-1\\\\-2y=-1-3\\\\-2y=-4\ \ /:(-2)\\\\y=2\\\\\begin{cases}x=1\\y=2\end{cases}[/tex]
[tex]c)\\\\\begin{cases}x+2y=6\\3x+6y=12\ \ /:(-3)\end{cases}\\\\\\+\begin{cases}x+2y=6\\-x-2y=-4\end{cases}\\---------\\0=2\\\\Uklad\ \ r\'owna\'n\ \ sprzeczny\ \ nie\ \ ma\ \ rozwiazania[/tex]
[tex]d)\\\\\begin{cases}-3x+4y=2\\6x+8y=-4\ \ /:2\end{cases}\\\\\\+\begin{cases}-3x+4y=2\\3x+4y=-2\end{cases}\\---------\\8y=0\ \ /:8\\y=0\\\\\\-3x+4\cdot0=2\\\\-3x+0=2\\\\-3x=2\ \ /:(-3)\\\\x=-\frac{2}{3}\\\\\begin{cases}x=-\frac{2}{3}\\y=0\end{cases}[/tex]
[tex]e)\\\\\begin{cases}y-x=-13\\\frac{1}{2}x-\frac{1}{3}y=5\ \ /\cdot6\end{cases}\\\\\\\begin{cases}-x+y=-13\ \ /\cdot2\\3x-2y=30\end{cases}\\\\\\+\begin{cases}-2x+2y=-26\\3x-2y=30\end{cases}\\----------\\x=4\\\\\\-4+y=-13\\\\y=-13+4\\\\y=-9\\\\\\\begin{cases}x=4\\y=-9\end{cases}[/tex]
[tex]f)\\\\\begin{cases}2x-\frac{3}{4}y=1\ \ /\cdot4\\5x+y=-7\end{cases}\\\\\\\begin{cases}8x-3y=4\\5x+y=-7\ \ /\cdot3\end{cases}\\\\\\+\begin{cases}8x-3y=4\\15x+3y=-21\end{cases}\\----------\\23x=-17\ \ /:23\\\\x=-\frac{17}{23}\\\\\\5\cdot(-\frac{17}{23})+y=-7\\\\-\frac{85}{23}+y=-7\\\\y=-7+\frac{85}{23}\\\\y=-7+3\frac{16}{23}\\\\y=-6\frac{23}{23}+3\frac{16}{23}\\\\y=-3\frac{7}{23}\\\\\begin{cases}x=-\frac{17}{23}\\y=-3\frac{7}{23}\end{cases}[/tex]
