a: \(\left\{{}\begin{matrix}x-y=3\\3x+y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-y+3x+y=3+1\\x-y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x=4\\y=x-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1-3=-2\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}2x+3y=10\\3x-5y=-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10x+15y=50\\9x-15y=-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}19x=38\\2x+3y=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\3y=10-2x=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=2\end{matrix}\right.\)
c: ĐKXĐ: x<>1 và y<>-2
\(\left\{{}\begin{matrix}\dfrac{3}{x-1}+\dfrac{1}{y+2}=1\\\dfrac{6}{x-1}-\dfrac{5}{y+2}=\dfrac{1}{4}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{15}{x-1}+\dfrac{5}{y+2}=5\\\dfrac{6}{x-1}-\dfrac{5}{y+2}=\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{21}{x-1}=5+\dfrac{1}{4}=\dfrac{21}{4}\\\dfrac{6}{x-1}-\dfrac{5}{y+2}=\dfrac{1}{4}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-1=4\\\dfrac{5}{y+2}=\dfrac{6}{x-1}-\dfrac{1}{4}=\dfrac{5}{4}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-1=4\\y+2=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=2\end{matrix}\right.\left(nhận\right)\)
