Odpowiedź:
[tex]Metoda\ \ podstawiania\\\\\begin{cases}\frac{2x-3y}{3}-\frac{x+3y}{6}=x-4y\ \ |\cdot6\\3x-4y=11\end{cases}\\\\\\\begin{cases}2(2x-3y)-(x+3y)=6x-24y\\3x-4y=11\end{cases}\\\\\\\begin{cases}4x-6y-x-3y=6x-24y\\3x-4y=11\end{cases}\\\\\\\begin{cases}3x-9y-6x+24y=0\\3x-4y=11\end{cases}\\\\\\\begin{cases}-3x+15y=0\ \ |:(-3)\\3x-4y=11\end{cases}\\\\\\\begin{cases}x-5y=0\\3x-4y=11\end{cases}\\\\\\\begin{cases}x=5y\\3x-4y=11\end{cases}[/tex]
[tex]3\cdot5y-4y=11\\\\15y-4y=11\\\\11y=11\ \ |:11\\\\y=1\\\\\\x=5\cdot1=5\\\\\\\begin{cases}x=5\\y=1\end{cases}[/tex]
[tex]Metoda\ \ przeciwnych\ \ wsp\'olczynnik\'ow\\\\\\\begin{cases}4(3x+y)-(x-2y)=3y+2x\\3(2x+3y)+7(x-y)=-28\end{cases}\\\\\\\begin{cases}12x+4y-x+2y=3y+2x\\6x+9y+7x-7y=-28\end{cases}\\\\\\\begin{cases}11x+6y-3y-2x=0\\13x+2y=-28\end{cases}\\\\\\\begin{cases}9x+3y=0\ \ |\cdot2\\13x+2y=-28\ \ |\cdot(-3)\end{cases}\\\\\\+\begin{cases}18x+6y=0\\-39x-6y=84\end{cases}\\----------\\-21x=84\ \ |:(-21)\\x=-4[/tex]
[tex]9\cdot(-4)+3y=0\\\\-36+3y=0\\\\3y=36\ \ |:3\\\\y=12\\\\\\\begin{cases}x=-4\\y=12\end{cases}[/tex]
