Câu 1: \(\left\{{}\begin{matrix}x+y=2\\2x-y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y+2x-y=2+1\\x+y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x=3\\y=2-x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\y=2-1=1\end{matrix}\right.\)
=>Chọn D
Câu 2:
\(\left\{{}\begin{matrix}x+y=1\\x-3y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y-x+3y=1-2\\x+y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4y=-1\\x=1-y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{1}{4}\\x=1-\left(-\dfrac{1}{4}\right)=1+\dfrac{1}{4}=\dfrac{5}{4}\end{matrix}\right.\)
=>Chọn C
Câu 3:
\(\left\{{}\begin{matrix}x+y=3\\x-2y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2y\\2y+y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3y=3\\x=2y\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=1\\x=2\cdot1=2\end{matrix}\right.\)
=>Chọn D
Câu 4:
\(\left\{{}\begin{matrix}3x-y=1\\-3x+y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-y=1\\3x-y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}0y=0\\y=3x-1\end{matrix}\right.\)
=>Hệ có vô số nghiệm
=>Chọn D
Câu 5:
\(\left\{{}\begin{matrix}x-y=3\\x-y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y-x+y=3-4\\x-y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}0x=1\\x-y=3\end{matrix}\right.\)
=>Hệ vô nghiệm
=>Chọn A
Câu 6:
\(\left\{{}\begin{matrix}x+2y=3\\2x-y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+4y=6\\2x-y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+4y-2x+y=6-1\\2x-y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\2x=y+1=1+1=2\end{matrix}\right.\)
=>x=1;y=1
=>Chọn B
