Odpowiedź:
[tex]a)\\\\\begin{cases}2x+y=4\\x+\frac{1}{2}y=2\end{cases}\\\\\\\begin{cases}y=4-2x\\x+\frac{1}{2}y=2\end{cases}\\\\\\x+\frac{1}{2}(4-2x)=2\\\\x+2-x=2\\\\2=2\\\\Uklad\ \ r\'owna\'n\ \ nieoznaczony\ \ (ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n)[/tex]
[tex]b)\\\\\begin{cases}2x+4y=-7\ \ /:2\\7x-3y=1\end{cases}\\\\\\\begin{cases}x+2y=-\frac{7}{2}\\7x-3y=1\end{cases}\\\\\\\begin{cases}x=-\frac{7}{2}-2y\\7x-3y=1\end{cases}\\\\\\7(-\frac{7}{2}-2y)-3y=1\\\\-\frac{49}{2}-14y-3y=1\\\\-17y=1+\frac{49}{2}\\\\-17y=\frac{2}{2}+\frac{49}{2}\\\\-17y=\frac{51}{2}\ \ /:(-17)\\\\y=-\frac{\not51^3}{2}\cdot\frac{1}{\not17_{1}}\\\\y=-\frac{3}{2}\\\\\\x=-\frac{7}{2}-\not2\cdot(-\frac{3}{\not2})\\\\x=-\frac{7}{2}+3\\\\x=-3\frac{1}{2}+3\\\\x=-\frac{1}{2}[/tex]
[tex]\begin{cases}x=-\frac{1}{2}\\y=-\frac{3}{2}\end{cases}\\\\\\\\c)\\\\\begin{cases}\frac{5x+2y}{3}-\frac{2x-1}{2}=1\ \ /\cdot6\\\frac{3-x}{2}-2y=3\ \ /\cdot2\end{cases}\\\\\\\begin{cases}2(5x+2y)-3(2x-1)=6\\3-x-4y=6\end{cases}\\\\\\\begin{cases}10x+4y-6x+3=6\\-x-4y=6-3\end{cases}\\\\\\\begin{cases}4x+4y=6-3\\-x-4y=3\ \ /\cdot(-1)\end{cases}\\\\\\\begin{cases}4x+4y=3\\x+4y=-3\end{cases}\\\\\\\begin{cases}4x+4y=3\\x=-3-4y\end{cases}\\\\\\4(-3-4y)+4y=3\\\\-12-16y+4y=3\\\\-12y=3+12\\\\-12y=15\ \ /:(-12)[/tex]
[tex]y=-\frac{15}{12}\\\\y=-\frac{5}{4}\\\\\\x=-3-\not4\cdot(-\frac{5}{\not4})\\\\x=-3+5\\\\x=2\\\\\begin{cases}x=2\\y=-\frac{5}{4}\end{cases}[/tex]
