Bài 1:
a) \(\left\{{}\begin{matrix}3x+y=3\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x=10\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\4-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-3\end{matrix}\right.\)
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b) \(\left\{{}\begin{matrix}x-y=3\\3x-4y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-3y=9\\3x-4y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=7\\x-y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=7\\x-7=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=7\\x=10\end{matrix}\right.\)
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c) \(\left\{{}\begin{matrix}4x+5y=-2\\2x-y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+5y=-2\\4x-2y=-16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x=-14\\2x-y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\-4-y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=4\end{matrix}\right.\)
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d) \(\left\{{}\begin{matrix}3x+y=3\\-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-\dfrac{5}{3}=3\\y=-\dfrac{5}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x=3+\dfrac{5}{3}=\dfrac{14}{3}\\y=-\dfrac{5}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{14}{9}\\y=-\dfrac{5}{3}\end{matrix}\right.\)
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Bài 2:
a) \(\left\{{}\begin{matrix}4x+y=2\\\dfrac{4}{3}x+\dfrac{1}{3}y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{3}x+\dfrac{1}{3}y=2\\\dfrac{4}{3}x+\dfrac{1}{3}y=1\end{matrix}\right.\) mà \(2\ne1\) \(\Rightarrow HPT\) vô nghiệm
b) \(\left\{{}\begin{matrix}x-y\sqrt{2}=0\\2x+y\sqrt{2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=y\sqrt{2}\\2x+x=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y\sqrt{2}=1\\x=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{\sqrt{2}}{2}\\x=1\end{matrix}\right.\)
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a.\(\left\{{}\begin{matrix}3x+y=3\\2x-y=7\end{matrix}\right.\)(=)\(\left\{{}\begin{matrix}5x=10\\2x-y=7\end{matrix}\right.\)
(=)\(\left\{{}\begin{matrix}x=2\\y=-3\end{matrix}\right.\)
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b.\(\left\{{}\begin{matrix}x-y=3\\3x-4y=2\end{matrix}\right.\)(=)\(\left\{{}\begin{matrix}x=3+y\\9+3y-4y=2\end{matrix}\right.\)
(=)\(\left\{{}\begin{matrix}x=3+y\\-y=-7\end{matrix}\right.\)(=)\(\left\{{}\begin{matrix}x=10\\y=7\end{matrix}\right.\)
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