《2025年轻松总复习暑假作业七年级综合人教版》

8. 已知方程组$\left\{\begin{array}{l} x + 2y = 4k,\\ 2x + y = 6 - k,\end{array} \right.若x + y = 2024$,则$k = $2022.

答案： 2022

9. 甲、乙、丙三个数的和是29,甲数比乙数大5,乙数的$\frac{1}{3}等于丙数的\frac{1}{2}$,则这三个数分别是14,9,6.

答案： 14,9,6

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

答案：
(1)$\left\{\begin{array}{l} x=\frac {60}{17},\\ y=\frac {12}{17}\end{array}\right. $
(2)$\left\{\begin{array}{l} x=\frac {26}{23},\\ y=\frac {8}{23}\end{array}\right. $

11. 已知$\left\{\begin{array}{l} x = 2,\\ y = 1\end{array} \right.是方程组\left\{\begin{array}{l} 2x + (m - 1)y = 2,\\ nx + y = 1\end{array} \right.$的解,求$(m + n)^{2025}$的值.

答案： 解:把$\left\{\begin{array}{l} x=2,\\ y=1\end{array}\right. $代入方程组,得:$\left\{\begin{array}{l} 4+(m-1)=2,\\ 2n+1=1,\end{array}\right. $解得$\left\{\begin{array}{l} m=-1,\\ n=0,\end{array}\right. $所以$(m+n)^{2025}=(-1)^{2025}=-1.$