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a: \(\left\{{}\begin{matrix}3x-2y=5\\-2x+y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-2y=5\\-4x+2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x=11\\-2x+y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-11\\y=2x+3=-22+3=-19\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}2x-y=4\\x-\dfrac{y}{2}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-y=4\\2x-y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}0y=0\left(luônđúng\right)\\2x-y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y\in R\\2x=y+4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y\in R\\x=\dfrac{1}{2}y+2\end{matrix}\right.\)
Vậy: \(\left\{{}\begin{matrix}y\in R\\x=\dfrac{y+4}{2}\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}3x+2y=-2\\5x+4y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x+4y=-4\\5x+4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-5x=-4-1=-5\\5x+4y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-5\\4y=1-5x=1+25=26\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=\dfrac{26}{4}=\dfrac{13}{2}\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}2x-y=6\\3x+5y=22\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10x-5y=30\\3x+5y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=52\\2x-y=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=4\\2x-y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2x-6=2\cdot4-6=2\end{matrix}\right.\)
e: \(\left\{{}\begin{matrix}-x+2y-6=0\\5x-3y-5=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x+2y=6\\5x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-5x+10y=30\\5x-3y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}7y=35\\x-2y=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\x=2y-6=10-6=4\end{matrix}\right.\)
g: \(\left\{{}\begin{matrix}2x-3y=8\\5x+2y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x-6y=16\\15x+6y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}19x=19\\2x-3y=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\3y=2x-8=2-8=-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\end{matrix}\right.\)
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