a)\(\left\{{}\begin{matrix}x-3y=-3\\2x+y=29\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}2x-6y=-6\\2x+y=29\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}-7y=-35\\2x+y=29\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=5\\2\cdot x+5=29\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=5\\x=12\end{matrix}\right.\)
Vậy hệ phương trình có nghiệm là (x;y), (12;5)
b)\(\left\{{}\begin{matrix}3x-y=5\\2x-3y=-13\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}6x-2y=10\\6x-9y=-39\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}7y=49\\6x-9y=-39\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=7\\6\cdot x-9\cdot7=-39\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=7\\x=4\end{matrix}\right.\)
Vậy hệ phương trình đã cho có nghiệm là (x;y), (4;7)
c)\(\left\{{}\begin{matrix}4x-3y=6\\x+y=5\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}4x-3y=6\\4x+4y=20\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}-7y=-14\\4x+4y=20\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=2\\4x+4\cdot2=20\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=3\end{matrix}\right.\)
Vậy hệ phương trình đã cho có nghieemjlaf (x;y),(3;2)
d)\(\left\{{}\begin{matrix}5x-2y=3\\x+4y=5\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}5x-2y=3\\5x+20y=25\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}-22y=-22\\5x+20y=25\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\x+20\cdot1=25\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=5\end{matrix}\right.\)
Vậy hệ phương trình đã cho có nghiệm là (x;y),(5;1)
