《2025年暑假作业知识出版社七年级数学华师大版》

5. 已知$a+b= 16,b+c= 12,c+a= 10$,则$a+b+c= $19.

答案： 19

6. 解下列方程组:
(1)$\left\{\begin{array}{l} x+y+z= 6,\\ z= 3,\\ 3x-y+z= 4;\end{array} \right. $
解：$\left\{\begin{array}{l} x=1,\\ y=2,\\ z=3.\end{array}\right. $
(2)$\left\{\begin{array}{l} 2x+y= 10,\\ x-y+z= 4,\\ 3x-y-z= 0.\end{array} \right. $
解：$\left\{\begin{array}{l} x=3,\\ y=4,\\ z=5.\end{array}\right. $

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

7. 某单位职工植树节去植树,甲、乙、丙三个小组共植树50棵,乙组植树的棵数是甲、丙两组的和的$\frac {1}{4}$,甲组植树的棵数恰是乙、丙两组的和,每组各植树多少棵?

答案： 解 设甲组植树$x$棵，乙组植树$y$棵，丙组植树$z$棵.
根据题意，得$\left\{\begin{array}{l} x+y+z=50,\\ y=\frac {1}{4}(x+z),\\ x=y+z.\end{array}\right. $
解得$\left\{\begin{array}{l} x=25,\\ y=10,\\ z=15.\end{array}\right. $
答：甲组植树 25 棵，乙组植树 10 棵，丙组植树 15 棵.

8. 由方程组$\left\{\begin{array}{l} 2x+y= 3,\\ 2y+z= 4,\\ 2z+x= 5\end{array} \right. 可以得到x+y+z$的值等于(C)
A. 6
B. 3
C. 4
D. 5

答案： C

9. 已知方程组$\left\{\begin{array}{l} 2x-y+z= 5,\\ 5x+8y-z= 9,\end{array} \right. 则x+y$的值为(B)
A. 14
B. 2
C. -14
D. -2

答案： B

10. 已知$|a-1|+|b+2|+(a+c-b)^{2}= 0$,则$a^{2}+b^{2}+c^{2}$等于(C)
A. 10
B. 12
C. 14
D. 16

答案： C