Câu 1:
\(\left\{{}\begin{matrix}2\left(x+1\right)+3\left(y-2\right)=9\\3\left(x-1\right)+y=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2+3y-6=9\\3x-3+y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+3y=9+6-2=13\\y=6-3x+3=-3x+9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-3x+9\\2x+3\left(-3x+9\right)=13\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-3x+9\\2x-9x+27=13\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-7x=-14\\y=-3x+9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-3\cdot2+9=9-6=3\end{matrix}\right.\)
Câu 2:
\(\left\{{}\begin{matrix}x\left(2y+1\right)-y\left(2x-2\right)=7\\x\left(2-2y\right)+y\left(2x+1\right)=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2xy+x-2xy+2y=7\\2x-2xy+2xy+y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+2y=7\\2x+y=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=7-2y\\2\left(7-2y\right)+y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=7-2y\\14-4y+y=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3y=14-8=6\\x=7-2y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=7-2\cdot2=7-4=3\end{matrix}\right.\)
Câu 3:
\(\left\{{}\begin{matrix}2\left(x+y\right)-3\left(y+1\right)=-7\\3\left(x+1\right)+2y=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2y-3y-3=-7\\3x+3+2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-y=-4\\3x+2y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=2x+4\\3x+2\left(2x+4\right)=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2x+4\\3x+4x+8=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=2x+4\\7x=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{5}{7}\\y=2\cdot\dfrac{-5}{7}+4=-\dfrac{10}{7}+4=\dfrac{18}{7}\end{matrix}\right.\)
Câu 4: \(\left\{{}\begin{matrix}3y\left(x-2\right)-x\left(3y+1\right)=5\\3x\left(2-y\right)+y\left(3x+2\right)=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3xy-6y-3xy-x=5\\6x-3xy+3xy+2y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-6y-x=5\\6x+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-6y-5\\6\left(-6y-5\right)+2y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-6y-5\\-36y-30+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-6y-5\\-34y=34\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-1\\x=-6\cdot\left(-1\right)-5=6-5=1\end{matrix}\right.\)
