《2025年假期园地暑假作业七年级数学人教版》

1. 下列属于二元一次方程组的是( )

A.$\left\{\begin{array}{l} 2a - b = 1,\\ \frac{2}{3} + 2b = 2.\end{array} \right.$
B.$\left\{\begin{array}{l} \frac{2}{a} - b = 2,\\ 2a + b = 4.\end{array} \right.$
C.$\left\{\begin{array}{l} 2a + b = 1,\\ ab = 3.\end{array} \right.$
D.$\left\{\begin{array}{l} a + 2b = 1,\\ b + 2c = 3.\end{array} \right.$

答案： A

2. 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.$\left\{\begin{array}{l} x = -2,\\ y = 3.\end{array} \right.$
C.$\left\{\begin{array}{l} x = 2,\\ y = 1.\end{array} \right.$
D.$\left\{\begin{array}{l} x = 2,\\ y = -1.\end{array} \right.$

答案： D

3. 方程组$\left\{\begin{array}{l} 3x - 4y = 2,\\ x + 2y = 1\end{array} \right.消去x所得y$的一元一次方程为( )

A.$3 - 2y - 1 - 4y = 2$
B.$3(1 - 2y) - 4y = 2$
C.$3(2y - 1) - 4y = 2$
D.$3 - 2y - 4y = 2$

答案： B

4. 已知$(x - 2y)^2 + |5x - 7y - 3| = 0$,则$x$,$y$的值是( )

A.$\left\{\begin{array}{l} x = 5,\\ y = 3.\end{array} \right.$
B.$\left\{\begin{array}{l} x = 1,\\ y = 2.\end{array} \right.$
C.$\left\{\begin{array}{l} x = 2,\\ y = 1.\end{array} \right.$
D.不能确定

答案： C

5. 若二元一次方程$2x + y = 3$,$3x - y = 2和2x - my = -1$有公共解,则$m$的值为( )

A.$-2$
B.$-1$
C.$3$
D.$4$

答案： C

6. 已知二元一次方程组为$\left\{\begin{array}{l} 2x + y = 7,\\ 2x + 2y = 8,\end{array} \right.则x - y = $____,$x + y = $____。

答案： 2 4

7. 已知$\left\{\begin{array}{l} x = 0,\\ y = -2,\end{array} \right. \left\{\begin{array}{l} x = 4,\\ y = 1\end{array} \right.都是方程ax + by = 8$的解,则$a = $____,$b = $____。

答案： 3 -4

8. $\left\{\begin{array}{l} x = 2,\\ y = -1\end{array} \right.是二元一次方程ax + by + 2 = 0$的一个解,则$2a - b - 6 = $____。

答案： -8

9. 班上有男、女同学共$71$人,女生人数的一半比男生人数少$20$人,若设男生人数为$x$人,女生人数为$y$人,列出方程组为____。

答案： $\begin{cases} x+y=71, \\ x-\dfrac{y}{2}=20. \end{cases}$

10. 某班有$40$名同学去看演出,购买甲、乙两种票共用去$370$元,其中甲种票每张$10$元,乙种票每张$8$元。设购买了甲种票$x$张,乙种票$y$张,由此可列出方程组____。

答案： $\begin{cases} x+y=40, \\ 10x+8y=370. \end{cases}$

11. 已知$|x - 8y| + 2(4y - 1)^2 + 3|8z - 3x| = 0$,则$x + y + z$的值为____。

答案： 3