b: ĐKXĐ: x<>0; y<>0
\(\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{4}{y}=2\\\dfrac{4}{x}-\dfrac{5}{y}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{12}{x}-\dfrac{16}{y}=8\\\dfrac{12}{x}-\dfrac{15}{y}=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{12}{x}-\dfrac{16}{y}-\dfrac{12}{x}+\dfrac{15}{y}=8-9=-1\\\dfrac{3}{x}-\dfrac{4}{y}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-\dfrac{1}{y}=-1\\\dfrac{3}{x}=\dfrac{4}{y}+2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\\dfrac{3}{x}=4+2=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=\dfrac{1}{2}\end{matrix}\right.\left(nhận\right)\)
a: ĐKXĐ: x<>0; y<>0
\(\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{1}{y}=7\\\dfrac{2}{x}+\dfrac{1}{y}=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{1}{y}+\dfrac{2}{x}+\dfrac{1}{y}=7+8\\\dfrac{2}{x}+\dfrac{1}{y}=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{5}{x}=15\\\dfrac{1}{y}=8-\dfrac{2}{x}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{3}\\\dfrac{1}{y}=8-2:\dfrac{1}{3}=8-6=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{1}{3}\\y=\dfrac{1}{2}\end{matrix}\right.\left(nhận\right)\)
e: ĐKXĐ: y<>2x; y<>-x
\(\left\{{}\begin{matrix}\dfrac{3}{2x-y}-\dfrac{6}{x+y}=-1\\\dfrac{1}{2x-y}-\dfrac{1}{x+y}=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3}{2x-y}-\dfrac{6}{x+y}=-1\\\dfrac{3}{2x-y}-\dfrac{3}{x+y}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{2x-y}-\dfrac{6}{x+y}-\dfrac{3}{2x-y}+\dfrac{3}{x+y}=-1-0\\\dfrac{1}{2x-y}-\dfrac{1}{x+y}=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-\dfrac{3}{x+y}=-1\\2x-y=x+y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y=3\\x-2y=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y-x+2y=3-0=3\\x+y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=2\end{matrix}\right.\left(nhận\right)\)
f: ĐKXĐ: x<>-1; y<>3
\(\left\{{}\begin{matrix}\dfrac{5x}{x+1}+\dfrac{y}{y-3}=27\\\dfrac{2x}{x+1}-\dfrac{3y}{y-3}=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{15x}{x+1}+\dfrac{3y}{y-3}=81\\\dfrac{2x}{x+1}-\dfrac{3y}{y-3}=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{15x}{x+1}+\dfrac{3y}{y-3}+\dfrac{2x}{x+1}-\dfrac{3y}{y-3}=81+4=85\\\dfrac{5x}{x+1}+\dfrac{y}{y-3}=27\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{17x}{x+1}=85\\\dfrac{y}{y-3}=27-\dfrac{5x}{x+1}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{x+1}=5\\\dfrac{y}{y-3}=27-5\cdot5=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+5=x\\2y-6=y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{5}{4}\\y=6\end{matrix}\right.\left(nhận\right)\)
