a:
ĐKXĐ: x<>0 và y<>0
\(\left\{{}\begin{matrix}\dfrac{2}{x}+\dfrac{1}{y}=2\\\dfrac{6}{x}-\dfrac{2}{y}=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{4}{x}+\dfrac{2}{y}=4\\\dfrac{6}{x}-\dfrac{2}{y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{10}{x}=5\\\dfrac{6}{x}-\dfrac{2}{y}=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{10}{5}=2\\\dfrac{2}{y}=\dfrac{6}{x}-1=\dfrac{6}{2}-1=3-1=2\end{matrix}\right.\)
=>x=2(nhận) và y=1(nhận)
b: ĐKXĐ: x<>-1
\(\left\{{}\begin{matrix}\dfrac{3}{x+1}-2y=-1\\\dfrac{5}{x+1}+3y=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{9}{x+1}-6y=-3\\\dfrac{10}{x+1}+6y=22\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{19}{x+1}=19\\\dfrac{5}{x+1}+3y=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+1=1\\3y=11-\dfrac{5}{x+1}=11-5=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=0\left(nhận\right)\\y=2\end{matrix}\right.\)
c: ĐKXĐ: y<>1
\(\left\{{}\begin{matrix}2x+\dfrac{3}{y-1}=5\\4x-\dfrac{1}{y-1}=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+\dfrac{3}{y-1}=5\\12x-\dfrac{3}{y-1}=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}14x=14\\4x-\dfrac{1}{y-1}=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\\dfrac{1}{y-1}=4x-3=4\cdot1-3=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\y-1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\left(nhận\right)\end{matrix}\right.\)
d: ĐKXĐ: y<>2
\(\left\{{}\begin{matrix}2x-\dfrac{3}{y-2}=-1\\3x+\dfrac{1}{y-2}=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-\dfrac{3}{y-2}=-1\\9x+\dfrac{3}{y-2}=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}11x=11\\3x+\dfrac{1}{y-2}=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\\dfrac{1}{y-2}=4-3x=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y-2=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=3\left(nhận\right)\\x=1\end{matrix}\right.\)
e: ĐKXĐ: x<>-1/2
\(\left\{{}\begin{matrix}\dfrac{2}{2x+1}-3y=7\\\dfrac{3}{2x+1}+2y=-9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{4}{2x+1}-6y=14\\\dfrac{9}{2x+1}+6y=-27\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{13}{2x+1}=-13\\\dfrac{2}{2x+1}-3y=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+1=-1\\3y=\dfrac{2}{2x+1}-7=-2-7=-9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1\left(nhận\right)\\y=-3\end{matrix}\right.\)
f: ĐKXĐ: y<>6
\(\left\{{}\begin{matrix}-2x+\dfrac{1}{6-y}=9\\3x-\dfrac{5}{6-y}=-10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-10x+\dfrac{5}{6-y}=45\\3x-\dfrac{5}{6-y}=-10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-7x=35\\3x-\dfrac{5}{6-y}=-10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-5\\\dfrac{5}{6-y}=3x+10=3\cdot\left(-5\right)+10=-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-5\\6-y=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=7\left(nhận\right)\end{matrix}\right.\)
