《2025年快乐过暑假江苏凤凰科学技术出版社七年级提优版》

1. 已知方程组$\left\{\begin{array}{l} 2x+y= 7,\\ x+2y= 8,\end{array} \right. 则x+y$的值是(A).
A.5
B.1
C.0
D.-1

答案： 1. A

2. 已知关于$x,y的二元一次方程组\left\{\begin{array}{l} 3x+2y= k+1,\\ x-2y= 9\end{array} \right. $的解互为相反数,则$k$的值是(B).
A.3
B.2
C.1
D.0

答案： 2. B

3. 已知方程组$\left\{\begin{array}{l} 2x+y= k-1,\\ x+2y= 2\end{array} \right. 的解满足x-y= 2$,则$k$的值是(D).
A.-1
B.1
C.3
D.5

答案： 3. D

4. 若关于$m,n的二元一次方程组\left\{\begin{array}{l} 2m+n= 3,\\ m-n= -1,\end{array} \right. 则m+2n= $4.

答案： 4. 4

5. 解下列方程组:
(1)$\left\{\begin{array}{l} x+1= y,\\ 2(x+1)= 5(y-1);\end{array} \right. $
解：$\begin{cases}x = \frac{2}{3},\\y = \frac{5}{3}.\end{cases}$
(2)$\left\{\begin{array}{l} 4x-(2y-3)= 9,\\ \frac {x}{3}-\frac {y+1}{2}= 1;\end{array} \right. $
解：$\begin{cases}x = 0,\\y = -3.\end{cases}$
(3)已知$\left\{\begin{array}{l} a_{1}x+b_{1}y= c_{1},\\ a_{2}x+b_{2}y= c_{2}\end{array} \right. $的解为$\left\{\begin{array}{l} x=3\\ y=4\end{array}\right. $，则关于x,y的方程组$\left\{\begin{array}{l} a_{1}(x+5)+b_{1}(y-3)= c_{1},\\ a_{2}(x+5)+b_{2}(y-3)= c_{2}\end{array}\right. $的解为____$\begin{cases}x = 8,\\y = 4\end{cases}$.

答案： 5.
(1) $\begin{cases}x + 1 = y,①\\2(x + 1) = 5(y - 1),②\end{cases}$
将①代入②，得 $2y = 5y - 5$，解得 $y = \frac{5}{3}$。
将 $y = \frac{5}{3}$ 代入①，得 $x = \frac{2}{3}$。
故原方程组的解为 $\begin{cases}x = \frac{2}{3},\\y = \frac{5}{3}.\end{cases}$
(2) $\begin{cases}4x - (2y - 3) = 9,\frac{x}{3} - \frac{y + 1}{2} = 1,\end{cases}$
原方程组可化为 $\begin{cases}2x - y = 3,①\\2x - 3y = 9,②\end{cases}$
① - ②，得 $y = -3$，
将 $y = -3$ 代入①，得 $2x + 3 = 3$，解得 $x = 0$。
故原方程组的解为 $\begin{cases}x = 0,\\y = -3.\end{cases}$
(3) $\begin{cases}x = 8,\\y = 4\end{cases}$