《2025年状元成才路创优作业八年级数学上册北师大版》

1. 用加减消元法解方程组$\begin{cases}x + y = -3,①\\3x + y = 6,②\end{cases} $由② - ①消去未知数$y$,所得到的一元一次方程是(A)
A.$2x = 9$
B.$2x = 3$
C.$4x = 9$
D.$4x = 3$

答案： A

2. 用加减消元法解方程组$\begin{cases}2x - 4y = 10,\\3x + 4y = 15,\end{cases} $较简便的消元方法是：将两个方程相加,消去未知数y。

答案： 相加 y

3. 方程组$\begin{cases}5x - 4y = 3,\\6x - 4y = 5\end{cases} $的解是$\left\{\begin{array}{l} x=2,\\ y=\frac {7}{4}\end{array}\right. $。

答案： $\left\{\begin{array}{l} x=2,\\ y=\frac {7}{4}\end{array}\right. $

4. 用加减消元法解下列方程组：
(1) [2024·广西中考]$\begin{cases}x + 2y = 3,①\\x - 2y = 1;②\end{cases} $
(2) [2024·苏州中考]$\begin{cases}2x + y = 7,①\\2x - 3y = 3。②\end{cases} $

答案：
(1)$\left\{\begin{array}{l} x=2,\\ y=\frac {1}{2}\end{array}\right. $
(2)$\left\{\begin{array}{l} x=3,\\ y=1。\end{array}\right. $

5. 用加减消元法解方程组$\begin{cases}x + 3y = 4,①\\3x - y = 2②\end{cases} $时,下列方法中无法消元的是(D)
A.①×3 - ②
B.②×3 + ①
C.①×(-3) + ②
D.① - ②×3

答案： D

6. 用加减消元法解下列方程组：
(1)$\begin{cases}2x + y = 2,①\\8x + 3y = 9;②\end{cases} $
(2) [2024·浙江中考]$\begin{cases}2x - y = 5,①\\4x + 3y = -10;②\end{cases} $
(3)$\begin{cases}2x + y = 3,①\frac{1}{2}x - \frac{3}{2}y = -1;②\end{cases} $
(4)$\begin{cases}4s - 3t = 1,①\\3s - 2t = -1。②\end{cases} $

答案：
(1)$\left\{\begin{array}{l} x=\frac {3}{2},\\ y=-1。\end{array}\right. $
(2)$\left\{\begin{array}{l} x=\frac {1}{2},\\ y=-4。\end{array}\right. $
(3)$\left\{\begin{array}{l} x=1,\\ y=1。\end{array}\right. $
(4)$\left\{\begin{array}{l} s=-5,\\ t=-7。\end{array}\right. $