1/ \(\left\{{}\begin{matrix}7x-3y=5\\\dfrac{x}{2}+\dfrac{y}{3}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7x-3y=5\\\dfrac{1}{2}x+\dfrac{1}{3}y=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{7}{3}x-y=\dfrac{5}{3}\\\dfrac{3}{2}x+y=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{23}{6}x=\dfrac{23}{3}\\7x-3y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
Vậy hệ phương trình có nghiệm duy nhất \(\left(x;y\right)=\left(2;3\right)\)
2/ \(\left\{{}\begin{matrix}3x+y=3\\2x-y=7\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x=10\\3x+y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-3\end{matrix}\right.\)
Vậy hệ phương trình có nghiệm duy nhất \(\left(x;y\right)=\left(2;-3\right)\)
3/ \(\left\{{}\begin{matrix}2x+y=5\\3x-2y=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x+2y=10\\3x-2y=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7x=21\\2x+y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-1\end{matrix}\right.\)
Vậy hệ phương trình có nghiệm duy nhất \(\left(x;y\right)=\left(3;-1\right)\)