3: \(\left\{{}\begin{matrix}3x-5y=-18\\x+2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-5y=-18\\3x+6y=15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-5y-3x-6y=-18-15\\x+2y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-11y=-33\\x=5-2y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=5-2\cdot3=-1\end{matrix}\right.\)
1: \(\left\{{}\begin{matrix}-x+3y=-10\\x-5y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x+3y+x-5y=-10+16\\x-5y=16\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2y=6\\x=5y+16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-3\\x=5\cdot\left(-3\right)+16=1\end{matrix}\right.\)
2: \(\left\{{}\begin{matrix}2x+y=7\\-x+4y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+y=7\\-2x+8y=20\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y-2x+8y=7+20\\2x+y=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9y=27\\2x=7-y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=\dfrac{7-y}{2}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\end{matrix}\right.\)
4: \(\left\{{}\begin{matrix}4x+3y=-6\\2x-5y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+3y=-6\\4x-10y=32\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+3y-4x+10y=-6-32\\2x-5y=16\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}17y=-38\\2x=5y+16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{38}{17}\\x=\dfrac{5y+16}{2}=\dfrac{41}{17}\end{matrix}\right.\)
5: \(\left\{{}\begin{matrix}2x-y=x+3y+3\\3x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-y-x-3y=3\\x-y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-4y=3\\x-y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-4y-x+y=3-3=0\\x-y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-3y=0\\x=y+3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=0\\x=0+3=3\end{matrix}\right.\)
6: \(\left\{{}\begin{matrix}2x-4y=3\\-x+2y=1\end{matrix}\right.\)
Vì \(\dfrac{2}{-1}=\dfrac{-4}{2}\ne\dfrac{3}{1}\)
nên hệ vô nghiệm
7: \(\left\{{}\begin{matrix}x+y=-2\left(x-1\right)\\7x+3y=x+y+5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y=-2x+2\\6x+2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+y=2\\6x+2y=5\end{matrix}\right.\)
Vì \(\dfrac{3}{6}=\dfrac{1}{2}\ne\dfrac{2}{5}\)
nên hệ vô nghiệm
8: \(\left\{{}\begin{matrix}2x+5y=-\left(x+y\right)\\6x+3y=y-10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+5y+x+y=0\\6x+3y-y=-10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+6y=0\\6x+2y=-10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x+12y=0\\6x+2y=-10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+12y-6x-2y=0-\left(-10\right)\\x+2y=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10y=10\\x=-2y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=-2\end{matrix}\right.\)
9: Vì \(\dfrac{3}{-9}=\dfrac{1}{-3}=\dfrac{-2}{6}\left(=-\dfrac{1}{3}\right)\)
nên hệ có vô số nghiệm
10: \(\left\{{}\begin{matrix}2x+5y=7\\2x-3y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+5y-2x+3y=7+1\\2x+5y=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}8y=8\\2x=7-5y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=\dfrac{7-5y}{2}=\dfrac{7-5}{2}=\dfrac{2}{2}=1\end{matrix}\right.\)
