Odpowiedź:
[tex]1)\\\\\begin{cases}x+y=5\\2x=5-2y\end{cases}\\\\\\\begin{cases}x=5-y\\2x=5-2y\end{cases}\\\\\\2(5-y)=5-2y\\\\10-2y=5-2y\\\\-2y+2y=5-10\\\\0=-5\\\\Uklad\ \ r\'owna\'n\ \ sprzeczny\ \ nie\ \ ma\ \ rozwiazania[/tex]
[tex]2)\\\\\begin{cases}2x-y-1=0\\x+2y-8=0\end{cases}\\\\\\\begin{cases}2x-y=1\\x+2y=8\end{cases}\\\\\\\begin{cases}2x-y=1\\x=8-2y\end{cases}\\\\\\2(8-2y)-y=1\\\\16-4y-y=1\\\\-5y=1-16\\\\-5y=-15\ \ /:(-5)\\\\y=3\\\\\\x=8-2\cdot3=8-6=2\\\\\begin{cases}x=2\\y=3\end{cases}[/tex]
[tex]3)\\\\\begin{cases}y=3x-2\\y=2x+3\end{cases}\\\\\\3x-2=2x+3\\\\3x-2x=3+2\\\\x=5\\\\\\y=2\cdot5+3=10+3=13\\\\\begin{cases}x=5\\y=13\end{cases}[/tex]
[tex]4)\\\\\begin{cases}7x-y+\sqrt{7}=0\\5x+6y=8\end{cases}\\\\\\\begin{cases}7x-y=-\sqrt{7}\\5x+6y=8\end{cases}\\\\\\\begin{cases}-y=-\sqrt{7}-7x\ \ /\cdot(-1)\\5x+6y=8\end{cases}\\\\\\\begin{cases}y=\sqrt{7}+7x\\5x+6y=8\end{cases}\\\\\\5x+6(\sqrt{7}+7x)=8\\\\5x+6\sqrt{7}+42x=8\\\\47x=8-6\sqrt{7}\ \ /:47\\\\x=\frac{8-6\sqrt{7}}{47}[/tex]
[tex]y=\sqrt{7}+7\cdot\frac{8-6\sqrt{7}}{47}\\\\y=\sqrt{7}+\frac{7(8-6\sqrt{7})}{47}\\\\y=\sqrt{7}+\frac{56-42\sqrt{7}}{47}\\\\y=\frac{47\sqrt{7}}{47}+\frac{56-42\sqrt{7}}{47}\\\\y=\frac{5\sqrt{7}+56}{47}\\\\\\\begin{cases}x=\frac{8-6\sqrt{7}}{47}\\y=\frac{5\sqrt{7}+56}{47}\end{cases}[/tex]
