答案：1.解:(1) $\begin{cases} 2x-y=14\textcircled{1},\\ x-4y=0\textcircled{2},\\ \end{cases}$
$\textcircled{2}×2-\textcircled{1}$,得$-7y=-14$,解得$y=2$.
把$y=2$代入$\textcircled{2}$,得$x=8$,所以原方程组的解为$\begin{cases} x=8,\\ y=2.\\ \end{cases}$
(2) $\begin{cases} 6x-5y=3\textcircled{1},\\ 6x+y=-15\textcircled{2},\\ \end{cases}$
$\textcircled{1}-\textcircled{2}$,得$-6y=18$,解得$y=-3$.
把$y=-3$代入$\textcircled{2}$,得$6x-3=-15$,解得$x=-2$,
所以原方程组的解为$\begin{cases} x=-2,\\ y=-3.\\ \end{cases}$

答案：2.解:(1) $\begin{cases} 3m-2n=5\textcircled{1},\\ 4m+2n=9\textcircled{2},\\ \end{cases}$
$\textcircled{1}+\textcircled{2}$,得$7m=14$,解得$m=2$.
把$m=2$代入$\textcircled{1}$,得$6-2n=5$,解得$n=\frac{1}{2}$.
所以原方程组的解为$\begin{cases} m=2,\\ n=\frac{1}{2}.\\ \end{cases}$
(2) $\begin{cases} 3x+7y=9\textcircled{1},\\ 4x-7y=5\textcircled{2},\\ \end{cases}$
$\textcircled{1}+\textcircled{2}$,得$7x=14$,解得$x=2$.
将$x=2$代入$\textcircled{1}$,得$6+7y=9$,解得$y=\frac{3}{7}$.
所以原方程组的解为$\begin{cases} x=2,\\ y=\frac{3}{7}.\\ \end{cases}$

答案：3.解:(1) $\begin{cases} x-y=2\textcircled{1},\\ 3x+2y=-19\textcircled{2},\\ \end{cases}$
$\textcircled{1}×2+\textcircled{2}$,得$5x=-15$,解得$x=-3$.
把$x=-3$代入$\textcircled{1}$,得$-3-y=2$,解得$y=-5$.
所以原方程组的解为$\begin{cases} x=-3,\\ y=-5.\\ \end{cases}$
(2) $\begin{cases} x+3y=7\textcircled{1},\\ 3x-6y=-4\textcircled{2},\\ \end{cases}$
$\textcircled{1}×2+\textcircled{2}$,得$5x=10$,解得$x=2$.
把$x=2$代入$\textcircled{1}$,得$2+3y=7$,解得$y=\frac{5}{3}$.
所以原方程组的解为$\begin{cases} x=2,\\ y=\frac{5}{3}.\\ \end{cases}$

答案：4.解:(1) $\begin{cases} 2x+3y=7\textcircled{1},\\ 3x+2y=3\textcircled{2},\\ \end{cases}$
$\textcircled{1}+\textcircled{2}$,得$5(x+y)=10$,则$x+y=2\textcircled{3}$,
$\textcircled{1}-\textcircled{3}×2$,得$y=3$,
$\textcircled{2}-\textcircled{3}×2$,得$x=-1$.
所以原方程组的解为$\begin{cases} x=-1,\\ y=3.\\ \end{cases}$
(2) $\begin{cases} 217x+314y=177\textcircled{1},\\ 314x+217y=177\textcircled{2},\\ \end{cases}$
$\textcircled{2}-\textcircled{1}$,得$(314-217)x+(217-314)y=0$,
化简,得$x-y=0$,即$x=y$.
把$x=y$代入$\textcircled{1}$,得$217x+314x=177$,解得$x=\frac{1}{3}$,
所以$y=\frac{1}{3}$.
所以原方程组的解为$\begin{cases} x=\frac{1}{3},\\ y=\frac{1}{3}.\\ \end{cases}$

答案：5.解:(1)化简方程组,得$\begin{cases} 2x-3y=17\textcircled{1},\\ 3x+2y=6\textcircled{2},\\ \end{cases}$
$\textcircled{1}×2+\textcircled{2}×3$,得$13x=52$,解得$x=4$.
把$x=4$代入$\textcircled{1}$,得$8-3y=17$,解得$y=-3$.
所以原方程组的解为$\begin{cases} x=4,\\ y=-3.\\ \end{cases}$
(2)由原方程组,得$\begin{cases} 2x+y=3\textcircled{1},\\ 2x-y=5\textcircled{2},\\ \end{cases}$
$\textcircled{1}+\textcircled{2}$,得$4x=8$,解得$x=2$.
$\textcircled{1}-\textcircled{2}$,得$2y=-2$,解得$y=-1$.
所以原方程组的解为$\begin{cases} x=2,\\ y=-1.\\ \end{cases}$