《2025年暑假零距离七年级数学人教版》

1. 二元一次方程组$\left\{\begin{array}{l} 3x+2y= 9,\\ x-2y= 3\end{array} \right. $的解是(D)
A.$\left\{\begin{array}{l} x= 1,\\ y= -1\end{array} \right. $
B.$\left\{\begin{array}{l} x= 3,\\ y= -1\end{array} \right. $
C.$\left\{\begin{array}{l} x= 5,\\ y= -3\end{array} \right. $
D.$\left\{\begin{array}{l} x= 3,\\ y= 0\end{array} \right. $

答案： D

2. 方程组$\left\{\begin{array}{l} 3x+y= 5,\\ x+3y= 7\end{array} \right. $的解为$\left\{\begin{array}{l} x=1,\\ y=2\end{array}\right. $。

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

3. 解方程组：
(1)$\left\{\begin{array}{l} 3x+2y= 12,\\ 2x-y= 1;\end{array} \right. $
(2)$\left\{\begin{array}{l} 4x+y= 5,\\ \frac {x-1}{2}+\frac {y}{3}= 2.\end{array} \right. $

答案：
(1) 解：$\left\{\begin{array}{l} 3x + 2y = 12, \quad①\\ 2x - y = 1. \quad②\end{array}\right.$
由②得：$y = 2x - 1$，③
将③代入①：$3x + 2(2x - 1) = 12$，
解得$x = 2$，
将$x = 2$代入③得$y = 3$，
$\therefore \left\{\begin{array}{l} x = 2,\\ y = 3.\end{array}\right.$
(2) 解：$\left\{\begin{array}{l} 4x + y = 5, \quad①\\ \frac{x - 1}{2} + \frac{y}{3} = 2. \quad②\end{array}\right.$
②×6化简：$3(x - 1) + 2y = 12$，即$3x + 2y = 15$，③
①×2 - ③：$8x + 2y - (3x + 2y) = 10 - 15$，
解得$x = -1$，
将$x = -1$代入①得$y = 9$，
$\therefore \left\{\begin{array}{l} x = -1,\\ y = 9.\end{array}\right.$

4. 若$\left\{\begin{array}{l} x= 1,\\ y= 2\end{array} \right. $是关于x,y的二元一次方程$ax-2y= 1$的解,则a的值为(B)
A.3
B.5
C.-3
D.-5

答案： B

5. 已知关于x,y的二元一次方程组$\left\{\begin{array}{l} 3x-y= 4m+1,\\ x+y= 2m-5\end{array} \right. 的解满足x-y= 4$,则m的值为(B)
A.0
B.1
C.2
D.3

答案： B

6. 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

7. 已知$\left\{\begin{array}{l} x= 2,\\ y= 3\end{array} \right. $是关于x,y的二元一次方程组$\left\{\begin{array}{l} mx+ny= 28,\\ mx-ny= 4\end{array} \right. $的解,则$6m+4n$的立方根为4。

答案： 4