\(\left\{{}\begin{matrix}2\left(3x+y\right)-3\left(x-2y\right)=14\\\dfrac{5x}{2}+\dfrac{2y}{3}=\dfrac{17}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x+2y-3x+6y=14\\\dfrac{15x+4y-34}{6}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x+8y=14\\15x+4y=34\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-15x-40y=-70\left(1\right)\\15x+4y=34\left(2\right)\end{matrix}\right.\)
Lấy \(\left(1\right)+\left(2\right):\)
\(\left\{{}\begin{matrix}-36y=36\\15x+4y=34\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-1\\15x+4y=34\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-1\\15x+4.\left(-1\right)=34\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x=\dfrac{38}{15}\end{matrix}\right.\)
Vậy hệ pt có nghiệm duy nhất \(\left(x;y\right)=\left(\dfrac{38}{15};-1\right)\)
