Odpowiedź:
[tex]c)\\\\\begin{cases}\frac{x-1}{2}+\frac{y+1}{3}=3\ \ /*6\\\frac{x+1}{3}-\frac{y-2}{6}=2\ \ /*6\end{cases}\\\\\\\begin{cases}3(x-1)+2(y+1)=18\\2(x+1)-(y-2)=12\end{cases}\\\\\\\begin{cases}3x-3+2y+2=18\\2x+2-y+2=12\end{cases}\\\\\\\begin{cases}3x-1+2y=18\\2x+4-y=12\end{cases}\\\\\\\begin{cases}3x+2y=18+1\\2x-y=12-4\end{cases}\\\\\\\begin{cases}3x+2y=19\\2x-y=8\ \ /*2\end{cases}\\\\\\+\begin{cases}3x+2y=19\\4x-2y=16\end{cases}\\---------\\7x=35 \ \ /:7\\x=5[/tex]
[tex]2*5-y=8\\\\10-y=8\\\\-y=8-10\\\\-y=-2\ \ \/*(-1)\\\\y=2\\\\\begin{cases}x=5\\y=2\end{cases}\\\\\\\\d)\\\\\begin{cases}2(x+1)=3(y-1)+13\\\frac{x-y}{3}=\frac{3x}{2}+\frac{3y}{4}+1\ \ /*12\end{cases}\\\\\\\begin{cases}2x+2=3y-3+13\\4(x-y)=18x+9y+12\end{cases}\\\\\\\begin{cases}2x-3y=10-2\\4x-4y-18x-9y=12\end{cases}\\\\\\\begin{cases}2x-3y=8\ \ /*7\\-14x-13y=12\end{cases}[/tex]
[tex]+\begin{cases}14x-21y=56\\-14x-13y=12\end{cases}\\----------\\-34y=68\ \ /:(-34)\\y=-2\\\\\\2x-3*(-2)=8\\\\2x+6=8\\\\2x=8-6\\\\2x=2\ \ /:2\\\\x=1\\\\\begin{cases}x=1\\y=-2\end{cases}\\\\\\\\e)\\\\\begin{cases}\frac{x+y}{2}=\frac{5y-x}{3}-\frac{7y-3x}{5}\ \ /*30\\5(x+1)=3(y-1)\end{cases}\\\\\\\begin{cases}15(x+y)=10(5y-x)-6(7y-3x)\\5x+5=3y-3\end{cases}\\\\\\\begin{cases}15x+15y=50y-10x-42y+18x\\5x-3y=-3-5\end{cases}[/tex]
[tex]\begin{cases}15x+15y-50y+10x+42y-18x=0\\5x-3y=-8\end{cases}\\\\\\\begin{cases}7x+7y=0\ \ /*(-5)\\5x-3y=-8\ \ /*7\end{cases}\\\\\\\begin{cases}-35x-35y=0\\35x-21y=-56\end{cases}\\\\\\-56y=-56\ \ /:(-56)\\y=1\\\\\\7x+7*1=0\\\\7x+7=0\\\\7x=-7\ \ /:7\\\\x=-1\\\\\begin{cases}x=-1\\y=1\end{cases}[/tex]
[tex]f)\\\\\begin{cases}\frac{x+y}{2}-\frac{x-y}{3}=1\ \ /*6\\\frac{5}{2}y-2=1-\frac{1}{2}x\ \ /*2\end{cases}\\\\\\\begin{cases}3(x+y)-2(x-y)=6\\5y-4=2-x\end{cases}\\\\\\\begin{cases}3x+3y-2x+2y=6\\5y+x=2+4\end{cases}\\\\\\\begin{cases}x+5y=6\ \ /*(-1)\\x+5y=6\end{cases}\\\\\\+\begin{cases}-x-5y=-6\\x+5y=6\end{cases}\\--------\\0=0\\\\Uklad\ \ r\'owna\'n\ \ to\.zsamo\'sciowy\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n[/tex]
