$解:(1)\begin{cases}{ 3x-y=13,①}\ \\ { 5x+2y=7,②} \end{cases}$
$由①,得y=3x-13,③\ $
$把③代入②,得5x+2(3x-13)=7,解得x=3,\ $
$把x=3代入③,得y=3×3-13=-4,\ $
$∴方程组的解$
$为\begin{cases}{\ x=3, }\ \\ { y=-4. } \end{cases}$
$(2)\begin{cases}{ \dfrac{x}{3}+1=y,①}\ \\ { 2(x+1)-y=6,②\ } \end{cases}$
$把①代入②,得2(x+1)-\frac{x}{3}-1=6,解得x=3,\ $
$把x=3代入①,得y=\frac{3}{3}+1=2,\ $
$∴方程组的解$
$为\begin{cases}{ x=3, }\ \\ { y=2. } \end{cases}$