《2025年桂壮红皮书暑假天地河北少年儿童出版社七年级数学》

1. 对于方程组$\begin{cases}3x+2y=-2①\\ 5x+2y=-4,②\end{cases}$由①-②,得(C)
A. $2x=2$
B. $2x=-6$
C. $-2x=2$
D. $-2x=-6$

答案： C

2. 方程组$\left\{\begin{array}{l} \frac {x}{3}=2-\frac {y}{2},\\ \frac {y+1}{4}=\frac {x}{5}-\frac {3}{4}\end{array}\right. $可以化简为(D)
A. $\left\{\begin{array}{l} 2x-3y=12,\\ 4x+5y=20\end{array}\right. $
B. $\left\{\begin{array}{l} 2x+3y=2,\\ 4x+5y=20\end{array}\right. $
C. $\left\{\begin{array}{l} 2x-3y=2,\\ 4x-5y=20\end{array}\right. $
D. $\left\{\begin{array}{l} 2x+3y=12,\\ 4x-5y=20\end{array}\right. $

答案： D

3. 我国古代数学名著《孙子算经》中记载了一道题,大意如下:100 匹马恰好拉了 100 片瓦,已知 1 匹大马能拉 3 片瓦,3 匹小马能拉 1 片瓦,有多少匹大马、多少匹小马? 如果设大马有 x 匹,小马有 y 匹,那么可列方程组为(C)
A. $\left\{\begin{array}{l} x+y=100,\\ 3x+3y=100\end{array}\right. $
B. $\left\{\begin{array}{l} x+y=100,\\ x+3y=100\end{array}\right. $
C. $\left\{\begin{array}{l} x+y=100,\\ 3x+\frac {1}{3}y=100\end{array}\right. $
D. $\left\{\begin{array}{l} x+y=100,\\ 3x+y=100\end{array}\right. $

答案： C

4. 用加减法解下列方程组时,可直接用①+②的是(C)
A. $\begin{cases}2x-3y=3,①\\3x-3y=4②\end{cases} $
B. $\begin{cases}x+\frac {1}{3}y=5,①\\ -\frac {1}{3}x-y=1②\end{cases}$
C. $\begin{cases}3m-5n=-4,①\\ 5m+5n=-4②\end{cases} $
D. $\begin{cases}x+2y=-3,①\\ 4x+y=6②\end{cases}$

答案： C

5. 若关于 x,y 的方程组$\left\{\begin{array}{l} 2x+3y=a+1,\\ 3x+2y=7\end{array}\right. $的解满足$x+y=4$,则$a=$12.

答案： 12

6. 若$(3x-2y+4)^{2}$与$|4x-y-3|$互为相反数,则$x=$2,$y=$5.

答案： 2 5

7. 用适当的方法解下列方程组:
(1)$\begin{cases}2x+y=5,①\\ x-3y=6;②\end{cases}$
解：$\left\{\begin{array}{l} x=3,\\ y=-1\end{array}\right. $
(2)$\begin{cases} 3x+4y=19①\\ x-y=4;②\end{cases}$
解：$\left\{\begin{array}{l} x=5,\\ y=1\end{array}\right. $
(3)$\begin{cases}2x+5y=3,①\\ 4x+11y=5②\end{cases}$
解：$\left\{\begin{array}{l} x=4,\\ y=-1\end{array}\right. $

答案：
(1)$\left\{\begin{array}{l} x=3,\\ y=-1\end{array}\right. $
(2)$\left\{\begin{array}{l} x=5,\\ y=1\end{array}\right. $
(3)$\left\{\begin{array}{l} x=4,\\ y=-1\end{array}\right. $