Question

Answer 1

a) \(\left\{{}\begin{matrix}3x-y=3\left(1\right)\\2x+y=7\left(2\right)\end{matrix}\right.\)

Lấy \(\left(1\right)+\left(2\right)\Rightarrow5x=10\Rightarrow x=2\Rightarrow y=7-4=3\)

Vậy hệ có nghiệm \(\left(x;y\right)\) là \(\left(2;3\right)\)

b) \(\left\{{}\begin{matrix}3x-y=5\\2y-x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x-y=5\left(1\right)\\6y-3x=0\left(2\right)\end{matrix}\right.\)

Lấy \(\left(1\right)+\left(2\right)\Rightarrow5y=5\Rightarrow y=1\Rightarrow x=2\)

Vậy hệ có nghiệm \(\left(x;y\right)\) là \(\left(2;1\right)\)

c) \(\left\{{}\begin{matrix}3x-y=5\\x+2y=4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x-y=5\left(1\right)\\3x+6y=12\left(2\right)\end{matrix}\right.\)

Lấy \(\left(2\right)-\left(1\right)\Rightarrow7y=7\Rightarrow y=1\Rightarrow x=4-2=2\)

Vậy hệ có nghiệm \(\left(x;y\right)\) là \(\left(2;1\right)\)

Answer 2

a) Ta có: \(\left\{{}\begin{matrix}3x-y=3\\2x+y=7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x=10\\2x+y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=7-2x=3\end{matrix}\right.\)

b) Ta có: \(\left\{{}\begin{matrix}3x-y=5\\-x+2y=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}6x-2y=10\\-x+2y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x=10\\-x+2y=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\2y=x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

c) Ta có: \(\left\{{}\begin{matrix}3x-y=5\\x+2y=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}6x-2y=10\\x+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x=14\\x+2y=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\2y=4-2=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)