《2025年名校课堂八年级数学上册北师大版》

1. 若关于 x,y 的方程组$\left\{\begin{array}{l} 3x+4y= 8,\\ mx+(2m-1)y= 7\end{array}\right. 的解也是二元一次方程x-2y= 1$的解,则 m 的值为 (A)
A.$\frac {5}{2}$
B.$\frac {3}{2}$
C.$\frac {1}{2}$
D. 1

答案： A

2. 已知关于 x,y 的方程组$\left\{\begin{array}{l} 2x+y= 6-2k,\\ x+2y= 2k-3\end{array}\right. 的解满足2x-y= 2k$,则 k 的值为 (A)
A.$\frac {7}{4}$
B.$\frac {3}{2}$
C.$\frac {4}{7}$
D.$\frac {2}{3}$

答案： A

3. 若满足方程组$\left\{\begin{array}{l} x+3y= m+2,\\ x-y= -1\end{array}\right. $的 x,y 互为相反数,则 m 的值为-1.

答案： -1

4. (2023·朝阳)已知关于 x,y 的方程组$\left\{\begin{array}{l} 2x+y= 2a+1,\\ x+2y= a-1\end{array}\right. 的解满足x-y= 4$,则 a 的值为2.

答案： 2

5. 已知关于 x,y 的方程组$\left\{\begin{array}{l} 4x+3y= 11,\\ ax+by= -2\end{array}\right. 和\left\{\begin{array}{l} 3x-5y= 1,\\ bx-ay= 6\end{array}\right. $的解相同,则$(a+b)^{2025}$的值为0.

答案： 0

6. 上数学课时,陈老师让同学们解一道关于 x,y 的方程组\left\{\begin{array}{l} ax+3y= -5,\enclose{circle} {1}\\ 2x-by= 14,\enclose{circle} {2}\end{array}\right. 并请小方和小龙两位同学到黑板上板演.可是小方同学看错了方程①中的 a,得到方程组的解为$\left\{\begin{array}{l} x= 3,\\ y= 2;\end{array}\right. $小龙同学看错了方程②中的 b,得到方程组的解为$\left\{\begin{array}{l} x= -2,\\ y= -1.\end{array}\right. $你能按正确的 a,b 值求出方程组的解吗? 请试一试.
解：将$\left\{\begin{array}{l} x=3\\ y=2\end{array}\right. $，代入②，得$6 - 2b = 14$，解得$b = $-4。将$\left\{\begin{array}{l} x=-2\\ y=-1\end{array}\right. $，代入①，得$-2a - 3 = - 5$，解得$a = $1。将$a = $1，$b = $-4代入原方程组，得$\left\{\begin{array}{l} x + 3y = - 5\\ 2x + 4y = 14\end{array}\right. $，解得$\left\{\begin{array}{l} x = $31,\\ y = $-12.\end{array}\right. $

答案： 解：将$\left\{\begin{array}{l} x=3\\ y=2\end{array}\right. $，代入②，得$6 - 2b = 14$，解得$b = - 4$。将$\left\{\begin{array}{l} x=-2\\ y=-1\end{array}\right. $，代入①，得$-2a - 3 = - 5$，解得$a = 1$。将$a = 1$，$b = - 4$代入原方程组，得$\left\{\begin{array}{l} x + 3y = - 5\\ 2x + 4y = 14\end{array}\right. $，解得$\left\{\begin{array}{l} x = 31\\ y = - 12\end{array}\right. $。