Odpowiedź:
[tex]a)\\\\\begin{cases}7(x-1)+8(y+1)=9\\6(x-1)+5(y+1)=7\end{cases}\\\\\\\begin{cases}7x-7+8y+8=9\\6x-6+5y+5=7\end{cases}\\\\\\\begin{cases}7x+1+8y=9\\6x-1+5y=7\end{cases}\\\\\\\begin{cases}7x+8y=9-1\\6x+5y=7+1\end{cases}\\\\\\\begin{cases}7x+8y=8\ \ /\cdot6\\6x+5y=8\ \ /\cdot(-7)\end{cases}\\\\\\+\begin{cases}42x+48y=48\\-42x-35y=-56\end{cases}\\-----------\\13y=-8\ \ /:13\\\\y=-\frac{8}{13}[/tex]
[tex]6x+5\cdot(-\frac{8}{13})=8\\\\6x-\frac{40}{13}=8\\\\6x=8+\frac{40}{13}\\\\6x=8+3\frac{1}{13}\\\\6x=11\frac{1}{13}\ \ /:6\\\\x=\frac{144}{13}:6\\\\x=\frac{\not144^2^4}{13}\cdot\frac{1}{\not6_{1}}\\\\x=\frac{24}{13}\\\\\\\begin{cases}x=\frac{24}{13}\\y=-\frac{8}{13}\end{cases}[/tex]
[tex]b)\\\\\begin{cases}2(x+1)+3(y-2)=5\\5(x+1)-6(y-2)=9\end{cases}\\\\\\\begin{cases}2x+2+3y-6=5\\5x+5-6y+12=9\end{cases}\\\\\\\begin{cases}2x-4+3y=5\\5x+17-6y=9\end{cases}\\\\\\\begin{cases}2x+3y=5+4\\5x-6y=9-17\end{cases}\\\\\\\begin{cases}2x+3y=9\ \ /\cdot2\\5x-6y=-8\end{cases}\\\\\\+\begin{cases}4x+6y=18\\5x-6y=-8\end{cases}\\---------\\9x=10\ \ /:9\\\\x=\frac{10}{9}[/tex]
[tex]2\cdot\frac{10}{9}+3y=9\\\\\frac{20}{9}+3y=9\\\\3y=9-\frac{20}{9}\\\\3y=\frac{81}{9}-\frac{20}{9}\\\\3y=\frac{61}{9}\ \ /:3\\\\y=\frac{61}{9}\cdot\frac{1}{3}\\\\y=\frac{61}{27}\\\\\\\begin{cases}x=\frac{10}{9}\\y=\frac{61}{27}\end{cases}[/tex]
[tex]c)\\\\\begin{cases}\frac{1}{10}(x+3)-\frac{1}{5}(y-3)=2\\\frac{1}{5}(x-2)+\frac{1}{4}(t-2)=0\end{cases}\\\\\\\begin{cases}\frac{1}{10}x+\frac{3}{10}-\frac{1}{5}y+\frac{3}{5}=2\ \ /\cdot10\\\frac{1}{5}x-\frac{2}{5}+\frac{1}{4}y-\frac{1}{2}=0\ \ /\cdot20\end{cases}\\\\\\\begin{cases}x+3-2y+6=20\\4x-8+5y-10=0\end{cases}\\\\\\\begin{cases}x+9-2y=20\\4x-18+5y=0\end{cases}\\\\\\\begin{cases}x-2y=20-9\\4x+5y=18\end{cases}\\\\\\\begin{cases}x-2y=11\ \ /\cdot(-4)\\4x+5y=18\end{cases}[/tex]
[tex]+\begin{cases}-4x+8y=-44\\4x+5y=18\end{cases}\\---------\\13y=-26\ \ /:13\\y=-2\\\\\\x-2\cdot(-2)=11\\\\x+4=11\\\\x=11-4\\\\x=7\\\\\\\begin{cases}x=7\\y=-2\end{cases}[/tex]
