1. (★★)由$\frac {x}{3}-\frac {y}{2}= 1$,可以得到用$x表示y$的式子为( )

A.$y= \frac {2x-2}{3}$
B.$y= \frac {2x}{3}-\frac {1}{3}$
C.$y= \frac {2x}{3}-2$
D.$y= 2-\frac {2x}{3}$

解：$\frac{x}{3}-\frac{y}{2}=1$
$2x - 3y = 6$
$-3y = 6 - 2x$
$y = \frac{2x - 6}{3}$
$y = \frac{2x}{3} - 2$
C

2. (★★★)方程组$\left\{\begin{array}{l} 3x+2y= 7,\\ 4x-y= 13\end{array} \right. $的解是( )

A.$\left\{\begin{array}{l} x= -1,\\ y= 3\end{array} \right. $
B.$\left\{\begin{array}{l} x= 3,\\ y= -1\end{array} \right. $
C.$\left\{\begin{array}{l} x= -3,\\ y= -1\end{array} \right. $
D.$\left\{\begin{array}{l} x= -1,\\ y= -3\end{array} \right. $

解：$\left\{\begin{array}{l} 3x+2y=7,\enclose{circle}{1}\\ 4x-y=13,\enclose{circle}{2}\end{array}\right.$
由②得，$y=4x-13$，③
将③代入①得，$3x+2(4x-13)=7$
解得$x=3$
将$x=3$代入③得，$y=4×3-13=-1$
$\therefore \left\{\begin{array}{l} x=3,\\ y=-1\end{array}\right.$
B

3. (★★★)方程组$\left\{\begin{array}{l} x-y= 1,\\ 2x+y= 5\end{array} \right. $的解是( )

A.$\left\{\begin{array}{l} x= -1,\\ y= 2\end{array} \right. $
B.$\left\{\begin{array}{l} x= 2,\\ y= -1\end{array} \right. $
C.$\left\{\begin{array}{l} x= 1,\\ y= 2\end{array} \right. $
D.$\left\{\begin{array}{l} x= 2,\\ y= 1\end{array} \right. $

解：$\left\{\begin{array}{l} x-y=1,①\\ 2x+y=5,②\end{array}\right.$
①+②，得3x=6，
解得x=2，
将x=2代入①，得2-y=1，
解得y=1，
$\therefore \left\{\begin{array}{l} x=2,\\ y=1\end{array}\right.$
D

4. (★★★)已知$x$,$y满足方程组\left\{\begin{array}{l} x+2y= 8,\\ 2x+y= 7,\end{array} \right. 则x+y与x-y$的值分别是( )

A.3,-1
B.5,-1
C.5,1
D.9,-1

【解析】：解方程组$\left\{\begin{array}{l} x + 2y = 8\\2x + y = 7\end{array}\right.$，将两个方程相加可得：$(x + 2y)+(2x + y)=8 + 7$，即$3x + 3y=15$，两边同时除以3得$x + y=5$；用第二个方程减去第一个方程可得：$(2x + y)-(x + 2y)=7 - 8$，即$x - y=-1$。
【答案】：B

5. (★★★)若方程$mx+ny= 6的两个解是\left\{\begin{array}{l} x= 1,\\ y= 1,\end{array} \right. $$\left\{\begin{array}{l} x= 2,\\ y= -1,\end{array} \right. 则m= $______,$n= $______．

【解析】：已知方程$mx + ny = 6$的两个解是$\begin{cases}x = 1\\y = 1\end{cases}$和$\begin{cases}x = 2\\y = -1\end{cases}$。
将$\begin{cases}x = 1\\y = 1\end{cases}$代入方程可得：$m×1 + n×1 = 6$，即$m + n = 6$ ①。
将$\begin{cases}x = 2\\y = -1\end{cases}$代入方程可得：$m×2 + n×(-1) = 6$，即$2m - n = 6$ ②。
① + ②得：$m + n + 2m - n = 6 + 6$，$3m = 12$，解得$m = 4$。
将$m = 4$代入①得：$4 + n = 6$，解得$n = 2$。
【答案】：4,2

6. (★★★)如果$|x-2y+1|+|x+y-5|= 0$,那么$x= $______,$y= $______．

解：∵|x-2y+1|+|x+y-5|=0
∴$\begin{cases}x-2y+1=0\\x+y-5=0\end{cases}$
由第二个方程得：x=5-y
将x=5-y代入第一个方程得：5-y-2y+1=0
解得y=2
将y=2代入x=5-y得：x=3
$x=3$，$y=2$

7. (★★★)解下列方程组．
(1)$\left\{\begin{array}{l} x-2y= 0,\\ 3x+2y= 8;\end{array} \right. $
(2)$\left\{\begin{array}{l} \frac {2x-y}{5}= 3,\\ \frac {x+y}{3}= 3;\end{array} \right. $
(3)$\left\{\begin{array}{l} 3x+4y= 2,\\ 2x-y= 5;\end{array} \right. $
(4)$\left\{\begin{array}{l} a+b= 3,\\ a+2b= 4.\end{array} \right. $

(1)解：$\left\{\begin{array}{l} x-2y=0①\\ 3x+2y=8②\end{array}\right.$
①+②得：$4x=8$
解得$x=2$
将$x=2$代入①得：$2-2y=0$
解得$y=1$
$\therefore \left\{\begin{array}{l} x=2\\ y=1\end{array}\right.$
(2)解：原方程组可化为$\left\{\begin{array}{l} 2x-y=15①\\ x+y=9②\end{array}\right.$
①+②得：$3x=24$
解得$x=8$
将$x=8$代入②得：$8+y=9$
解得$y=1$
$\therefore \left\{\begin{array}{l} x=8\\ y=1\end{array}\right.$
(3)解：$\left\{\begin{array}{l} 3x+4y=2①\\ 2x-y=5②\end{array}\right.$
由②得：$y=2x-5$③
将③代入①得：$3x+4(2x-5)=2$
$3x+8x-20=2$
$11x=22$
解得$x=2$
将$x=2$代入③得：$y=2×2-5=-1$
$\therefore \left\{\begin{array}{l} x=2\\ y=-1\end{array}\right.$
(4)解：$\left\{\begin{array}{l} a+b=3①\\ a+2b=4②\end{array}\right.$
②-①得：$b=1$
将$b=1$代入①得：$a+1=3$
解得$a=2$
$\therefore \left\{\begin{array}{l} a=2\\ b=1\end{array}\right.$