《2025年名校课堂八年级数学上册北师大版》

1. 用代入消元法解方程组$\left\{\begin{array}{l} x= 2y,①\\ y-x= 3②\end{array}\right. $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. 对于二元一次方程组$\left\{\begin{array}{l} y= x-1,①\\ x+2y= 7,②\end{array}\right. $将①式代入②式,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$\left\{\begin{array}{l} x+2y= 5,\\ y= 2x\end{array}\right. $的解是$\left\{\begin{array}{l} x = 1,\\ y = 2\end{array}\right.$.

答案： $\left\{\begin{array}{l} x = 1,\\ y = 2\end{array}\right.$

4. 用代入消元法解方程组:
(1)$\left\{\begin{array}{l} y= x-4,\enclose{circle} {1}\\ x+y= 6.\enclose{circle} {2}\end{array}\right.$
解：将①代入②，得$x+(x - 4)=6$。解得$x = 5$。将$x = 5$代入①，得$y = 1$。∴原方程组的解为$\left\{\begin{array}{l} x = 5,\\ y = 1.\end{array}\right.$
(2)$\left\{\begin{array}{l} 4x-y= 1,\enclose{circle} {1}\\ y= 2x+3.\enclose{circle} {2}\end{array}\right.$
解：将②代入①，得$4x-(2x + 3)=1$。解得$x = 2$。将$x = 2$代入②，得$y = 7$。∴原方程组的解为$\left\{\begin{array}{l} x = 2,\\ y = 7.\end{array}\right.$
(3)$\left\{\begin{array}{l} x= \frac {y+1}{3},\enclose{circle} {1}\\ 6x-y= 4.\enclose{circle} {2}\end{array}\right.$
解：将①代入②，得$2(y + 1)-y = 4$。解得$y = 2$。将$y = 2$代入①，得$x = 1$。∴原方程组的解为$\left\{\begin{array}{l} x = 1,\\ y = 2.\end{array}\right.$

答案： 解：
(1)将①代入②，得$x+(x - 4)=6$。解得$x = 5$。将$x = 5$代入①，得$y = 1$。
∴原方程组的解为$\left\{\begin{array}{l} x = 5,\\ y = 1.\end{array}\right.$
(2)将②代入①，得$4x-(2x + 3)=1$。解得$x = 2$。将$x = 2$代入②，得$y = 7$。
∴原方程组的解为$\left\{\begin{array}{l} x = 2,\\ y = 7.\end{array}\right.$
(3)将①代入②，得$2(y + 1)-y = 4$。解得$y = 2$。将$y = 2$代入①，得$x = 1$。
∴原方程组的解为$\left\{\begin{array}{l} x = 1,\\ y = 2.\end{array}\right.$

5. 用代入消元法解方程组:$\left\{\begin{array}{l} 2x+y= 4,①\\ 3x-2y= 13.②\end{array}\right.$
解:由①,得$y=$$-2x + 4$.③
将③代入②,得$3x-$$2(-2x + 4)$$=13$,
解得$x=$3.
将$x=$3代入③,得$y=$-2.
∴原方程组的解为$\left\{\begin{array}{l} x = 3,\\ y = -2\end{array}\right.$.

答案： $-2x + 4$ $2(-2x + 4)$ 3 3 ③ -2 $\left\{\begin{array}{l} x = 3,\\ y = -2\end{array}\right.$

6. 方程组$\left\{\begin{array}{l} 2x= 3y,\\ y-4x= 10\end{array}\right. $的解是 (C)
A. $\left\{\begin{array}{l} x= 3,\\ y= 2\end{array}\right. $
B. $\left\{\begin{array}{l} x= 3,\\ y= -2\end{array}\right. $
C. $\left\{\begin{array}{l} x= -3,\\ y= -2\end{array}\right. $
D. $\left\{\begin{array}{l} x= -3,\\ y= 2\end{array}\right. $

答案： C

7. 用代入消元法解方程组:
(1)(2024·浙江)$\left\{\begin{array}{l} 2x-y= 5,\enclose{circle} {1}\\ 4x+3y= -10.\enclose{circle} {2}\end{array}\right.$
解：由①，得$y = 2x - 5$。③将③代入②，得$4x + 3(2x - 5)=-10$，解得$x=\frac{1}{2}$。将$x=\frac{1}{2}$代入③，得$y = -4$。∴原方程组的解为$\left\{\begin{array}{l} x=\frac{1}{2},\\ y = -4.\end{array}\right.$
(2)$\left\{\begin{array}{l} 7x+3y= 2,\enclose{circle} {1}\\ 2x+y= 3.\enclose{circle} {2}\end{array}\right.$
解：由②，得$y = 3 - 2x$。③将③代入①，得$7x+3(3 - 2x)=2$。解得$x = -7$。将$x = -7$代入③，得$y = 17$。∴原方程组的解为$\left\{\begin{array}{l} x = -7,\\ y = 17.\end{array}\right.$

答案： 解：
(1)由①，得$y = 2x - 5$。③将③代入②，得$4x + 3(2x - 5)=-10$，解得$x=\frac{1}{2}$。将$x=\frac{1}{2}$代入③，得$y = -4$。
∴原方程组的解为$\left\{\begin{array}{l} x=\frac{1}{2},\\ y = -4.\end{array}\right.$
(2)由②，得$y = 3 - 2x$。③将③代入①，得$7x+3(3 - 2x)=2$。解得$x = -7$。将$x = -7$代入③，得$y = 17$。
∴原方程组的解为$\left\{\begin{array}{l} x = -7,\\ y = 17.\end{array}\right.$