《2025年暑假综合练习河北人民出版社七年级数学》

1. 若方程$(m - 2)x = 3y + 4是关于x$,$y$的二元一次方程,则$m$的取值范围是 (B)
A.$m \neq 0$
B.$m \neq 2$
C.$m \neq - 3$
D.$m \neq 3$

答案： B

2. 下列方程组中,是二元一次方程组的是 (C)
A.$\left\{\begin{array}{l} x = 2y - 1,\\ y = 3 - z\end{array} \right.$
B.$\left\{\begin{array}{l} x + y = 12,\\ xy = 35\end{array} \right.$
C.$\left\{\begin{array}{l} x = 1,\\ y = - 1\end{array} \right.$
D.$\left\{\begin{array}{l} x - y = 2,\\ \frac{1}{x} - \frac{1}{y} = 1\end{array} \right.$

答案： C

3. 已知$\left\{\begin{array}{l} x = - 1,\\ y = 3,\end{array} \right. \left\{\begin{array}{l} x = 1,\\ y = 2,\end{array} \right. \left\{\begin{array}{l} x = 3,\\ y = 1\end{array} \right.$是二元一次方程$x + 2y = 5$的三个解,$\left\{\begin{array}{l} x = - 1,\\ y = - 2,\end{array} \right. $$\left\{\begin{array}{l} x = 1,\\ y = 2,\end{array} \right. \left\{\begin{array}{l} x = 3,\\ y = 6\end{array} \right.$是二元一次方程$2x - y = 0$的三个解,则方程组$\left\{\begin{array}{l} x + 2y = 5,\\ 2x - y = 0\end{array} \right.$的解是 (D)
A.$\left\{\begin{array}{l} x = - 1,\\ y = 3\end{array} \right.$
B.$\left\{\begin{array}{l} x = - 1,\\ y = - 2\end{array} \right.$
C.$\left\{\begin{array}{l} x = 3,\\ y = 6\end{array} \right.$
D.$\left\{\begin{array}{l} x = 1,\\ y = 2\end{array} \right.$

答案： D

4. 如果$|x + y - 1|和(2x + y - 3)^{2}$互为相反数,那么$x$,$y$的值为 (A)
A.$\left\{\begin{array}{l} x = 2,\\ y = - 1\end{array} \right.$
B.$\left\{\begin{array}{l} x = - 1,\\ y = - 2\end{array} \right.$
C.$\left\{\begin{array}{l} x = 1,\\ y = 2\end{array} \right.$
D.$\left\{\begin{array}{l} x = - 2,\\ y = - 1\end{array} \right.$

答案： A

5. 已知关于$x$,$y的二元一次方程组\left\{\begin{array}{l} x - y = 3m,\\ x + 3y = 4 - m,\end{array} \right.$下列说法正确的是 ( D )
甲：当这个方程组的解$x$,$y$的值互为相反数时,$m = - 2$；
乙：当$m = 1$时,方程组的解也是方程$x + y = 4 + 2m$的解；
丙：无论$m$取什么数,$x + 2y$的值始终不变；
丁：若用含$x的代数式表示y$,则有$y = - \frac{x}{2} + \frac{3}{2}$.
A.甲和丙
B.乙和丙
C.乙、丙和丁
D.甲、丙和丁

答案： D