a: \(\left\{{}\begin{matrix}\dfrac{1}{2}x+y=1\\3x+2y=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+2y=2\\3x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2y=2-x\\3x+2-x=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2y=2-x\\2x+2=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\2y=2-4=-2\end{matrix}\right.\)
=>x=4 và y=-1
b: \(\left\{{}\begin{matrix}\dfrac{y}{5}-\dfrac{x-y}{2}=\dfrac{1}{10}\\\dfrac{y}{2}-\dfrac{x+y}{5}=\dfrac{1}{5}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{2y-5\left(x-y\right)}{10}=\dfrac{1}{10}\\\dfrac{5y-2\left(x+y\right)}{10}=\dfrac{1}{5}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2y-5x+5y=1\\5y-2x-2y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-5x+7y=1\\-2x+5y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10x-14y=-2\\10x-25y=-10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}10x=14y-2\\14y-2-25y=-10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-11y=-8\\10x=14y-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{8}{11}\\10x=14\cdot\dfrac{8}{11}-2=\dfrac{90}{11}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{9}{11}\\y=\dfrac{8}{11}\end{matrix}\right.\)
c: ĐKXĐ: x<>-8 và y<>-4
\(\left\{{}\begin{matrix}\dfrac{x}{2}-\dfrac{y}{3}=0\\\dfrac{4}{y+4}=\dfrac{9}{x+8}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-2y=0\\4\left(x+8\right)=9\left(y+4\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-2y=0\\4x+32-9y-36=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-2y=0\\4x-9y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}12x-8y=0\\12x-27y=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x=8y\\8y-27y=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-19y=12\\x=\dfrac{2}{3}y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{12}{19}\\x=\dfrac{2}{3}\cdot\dfrac{-12}{19}=-\dfrac{8}{19}\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}x-y=20\\x-\dfrac{x}{8}=y+\dfrac{x}{8}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=x-20\\\dfrac{7}{8}x=x-20+\dfrac{x}{8}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=x-20\\-\dfrac{1}{4}x=-20\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=80\\y=80-20=60\end{matrix}\right.\)
