Giải các hệ phương trình sau :
a, \(\begin{cases}5x-4y=3\\7x-9y=8\end{cases}\)
b, \(\begin{cases}\frac{1}{x}-\frac{8}{y}=18\\\frac{5}{x}+\frac{4}{y}=51\end{cases}\)
c, \(\begin{cases}\frac{10}{x-1}+\frac{1}{y+2}=1\\\frac{25}{x-1}+\frac{3}{y+2}=2\end{cases}\)
d, \(\begin{cases}\frac{27}{2x-y}+\frac{32}{x+3y}=7\\\frac{45}{2x-y}-\frac{48}{x+3y}=-1\end{cases}\)
a: \(\Leftrightarrow\left\{{}\begin{matrix}35x-28y=21\\35x-45y=40\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}17y=-19\\5x-4y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{19}{17}\\x=-\dfrac{5}{17}\end{matrix}\right.\)
b: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}-\dfrac{8}{y}=18\\\dfrac{10}{x}+\dfrac{8}{y}=102\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{11}{x}=120\\\dfrac{1}{x}-\dfrac{8}{y}=18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{11}{120}\\y=-\dfrac{44}{39}\end{matrix}\right.\)
c: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{30}{x-1}+\dfrac{3}{y+2}=3\\\dfrac{25}{x-1}+\dfrac{3}{y+2}=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5}{x-1}=1\\\dfrac{10}{y-1}+\dfrac{1}{y+2}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=5\\\dfrac{1}{y+2}+2=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=-3\end{matrix}\right.\)
d: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{135}{2x-y}+\dfrac{160}{x+3y}=35\\\dfrac{135}{2x-y}-\dfrac{144}{x+3y}=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+3y=8\\2x-y=9\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+6y=16\\2x-y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=5\end{matrix}\right.\)
