《2025年状元成才路创优作业八年级数学上册北师大版》

1. 用代入消元法解方程组$\begin{cases}x = 2y, &①\\3y - x = 2 &②\end{cases} $时,下列说法正确的是(B)
A.直接把①代入②,消去$y$
B.直接把①代入②,消去$x$
C.直接把②代入①,消去$y$
D.直接把②代入①,消去$x$

答案： B

2. 对于方程组$\begin{cases}y = x - 1, &①\\x + 2y = 7, &②\end{cases} $将①代入②,消去$y$可以得到(B)
A.$x + 2x - 1 = 7$
B.$x + 2x - 2 = 7$
C.$x + x - 1 = 7$
D.$x + 2x + 2 = 7$

答案： B

3. 二元一次方程组$\begin{cases}4x + y = 7,\\y = 3x\end{cases} $的解是$\left\{\begin{array}{l} x=1,\\ y=3\end{array}\right. $。

答案： $\left\{\begin{array}{l} x=1,\\ y=3\end{array}\right. $

4. 用代入消元法解下列方程组：
(1)$\begin{cases}2x - y = 2, &①\\x = 2y + 4; &②\end{cases} $
(2)$\begin{cases}2y - 3x = 8, &①\\y = \dfrac{x + 4}{2}。 &②\end{cases} $

答案： 解:
(1)$\left\{\begin{array}{l} x=0,\\ y=-2。\end{array}\right. $
(2)$\left\{\begin{array}{l} x=-2,\\ y=1。\end{array}\right. $

5. 用代入消元法解方程组$\begin{cases}2x - y = 7, &①\\3x - 4y = 3, &②\end{cases} $使得代入后,化简比较容易的变形是(B)
A.由①,得$x = \dfrac{7 + y}{2}$
B.由①,得$y = 2x - 7$
C.由②,得$x = \dfrac{3 + 4y}{3}$
D.由②,得$y = \dfrac{3x - 3}{4}$

答案： B

6. 用代入消元法解下列方程组：
(1)$\begin{cases}x + y = 0, &①\\4x - y = 5; &②\end{cases} $
(2)$\begin{cases}2x - 3y = 3, &①\\4x - y = - 4; &②\end{cases} $
(3)$\begin{cases}3y = 7 + x, &①\\2x = 5y; &②\end{cases} $
(4)$\begin{cases}2m + n = 2, &①\\8m + 3n = 9。 &②\end{cases} $

答案： 解:
(1)$\left\{\begin{array}{l} x=1,\\ y=-1。\end{array}\right. $
(2)$\left\{\begin{array}{l} x=-\frac {3}{2},\\ y=-2。\end{array}\right. $
(3)$\left\{\begin{array}{l} x=35,\\ y=14。\end{array}\right. $
(4)$\left\{\begin{array}{l} m=\frac {3}{2},\\ n=-1。\end{array}\right. $