\(a,\left\{{}\begin{matrix}-2x+y=5\\x+3y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-2x+y=5\\x=1-3y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-2\left(1-3y\right)+y=5\\x+3y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-2+6y+y=5\\x+3y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7y=7\\x+3y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\x+3.1=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=-2\end{matrix}\right.\)
Vậy hệ pt có nghiệm duy nhất \(\left(x;y\right)=\left(-2;1\right)\)
\(b,\left\{{}\begin{matrix}x-2y=4\\-3x+6y=-12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4+2y\\-3\left(4+2y\right)+6y=-12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2y=4\\-12-6y+6y=-12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2y=4\\0=0\left(LD\right)\end{matrix}\right.\) ( LD : luôn đúng )
Vậy hệ pt có vô số nghiệm.
