《2025年新课堂学习与探究八年级数学上册北师大版》

1. (宿迁中考)若关于$x,y的二元一次方程组\begin{cases}ax + y = b,\\cx - y = d\end{cases} 的解是\begin{cases}x = 3,\\y = -2,\end{cases} 则关于x,y的方程组\begin{cases}ax + 2y = 2a + b,\\cx - 2y = 2c + d\end{cases} $的解是$\left\{\begin{array}{l} x=5,\\ y=-1\end{array}\right. $.

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

2. (安顺中考)若$a + 2b = 8,3a + 4b = 18$,则$a + b$的值为5.

答案： 5

3. (苏州中考)解方程组：$\begin{cases}2x + y = 7,\\2x - 3y = 3.\end{cases} $

答案： 解:$\left\{\begin{array}{l} 2x+y=7①,\\ 2x-3y=3②,\end{array}\right. $$①-②$得$4y=4,y=1,$将$y=1$代入①得$x=3,$故方程组的解为$\left\{\begin{array}{l} x=3,\\ y=1.\end{array}\right. $