《2025年点拨训练七年级数学上册沪科版安徽专版》

3. (14 分) 思维可视化 如何解方程组：
$\begin{cases}\dfrac{2}{3}(2x + y) = 4,① \\ \dfrac{3}{4}x + \dfrac{5}{6}(2x + y) = 8.②\end{cases} $
思维过程

6；$\frac {3}{4}x+\frac {5}{6}×6=8$；4；4；$2×4+y=6$；-2；$\left\{\begin{array}{l} x=4,\\ y=-2\end{array}\right. $

答案： 3. 6；$\frac {3}{4}x+\frac {5}{6}×6=8$；4；4；$2×4+y=6$；-2；$\left\{\begin{array}{l} x=4,\\ y=-2\end{array}\right. $

4. (8 分) 解方程组：$\begin{cases}3x + 2(x + y) = -1,① \\ 3y - 4(x + y) = 5.②\end{cases} $

答案： 4. 解：方程组的解为$\left\{\begin{array}{l} x=-3,\\ y=7.\end{array}\right. $

5. (8 分) 解方程组：$\begin{cases}(\dfrac{a}{3} - 1) + 2(\dfrac{b}{5} + 2) = 4, \\ 2(\dfrac{a}{3} - 1) + (\dfrac{b}{5} + 2) = 5.\end{cases} $

答案： 5. 解：令$\frac {a}{3}-1=m,\frac {b}{5}+2=n$.则原方程组可变为$\left\{\begin{array}{l} m+2n=4,\\ 2m+n=5,\end{array}\right. $解得$\left\{\begin{array}{l} m=2,\\ n=1,\end{array}\right. $即$\left\{\begin{array}{l} \frac {a}{3}-1=2,\\ \frac {b}{5}+2=1,\end{array}\right. $解得$\left\{\begin{array}{l} a=9,\\ b=-5.\end{array}\right. $

6. (12 分) 中考趋势·阅读理解 (1) 仔细阅读下面解方程组的方法,并将解题过程补充完整：
解方程组$\begin{cases}19x + 18y = 17,① \\ 17x + 16y = 15②\end{cases} $时,直接采用代入消元法或加减消元法,计算会很复杂,若采用下面的解法,则会简单很多.
解：① - ②,得2x + 2y = 2,即x + y = 1,③
③× 16,得16x + 16y = 16,④
② - ④,得x=-1.
将x=-1代入③,得y=2.
所以方程组的解为；
(2) 请你采用上述方法解方程组：
$\begin{cases}2026x + 2025y = 2024,① \\ 2024x + 2023y = 2022.②\end{cases} $
解：① - ②，得2x + 2y = 2，即x + y = 1，③
③×2023，得2023x + 2023y = 2023，④
② - ④，得x = -1
将x = -1代入③，得-1 + y = 1，解得y = 2

答案： 6. 解：
(1)-1；-1；2；$\left\{\begin{array}{l} x=-1,\\ y=2\end{array}\right. $
(2)方程组的解为$\left\{\begin{array}{l} x=-1,\\ y=2.\end{array}\right. $
(3)方程组的解为$\left\{\begin{array}{l} x=-1,\\ y=2.\end{array}\right. $