《2025年暑假零距离七年级数学人教版》

1. 下列方程组中是二元一次方程组的是(C)
A.$\left\{\begin{array}{l} x^{2}+3y= 1,\\ 2x-y= 4\end{array} \right. $
B.$\left\{\begin{array}{l} xy= 2,\\ x+2y= 5\end{array} \right. $
C.$\left\{\begin{array}{l} m+3n= 10,\\ 5m-2n= 1\end{array} \right. $
D.$\left\{\begin{array}{l} a-b= 6,\\ b+c= 3\end{array} \right. $

答案： C

2. 已知x,y满足方程组$\left\{\begin{array}{l} x+2y= 12,\\ 2x+y= -15,\end{array} \right. 则(x+y)^{2025}$的值为(B)
A.2 025
B.-1
C.1
D.-2 025

答案： B

3. 利用加减消元法解方程组$\left\{\begin{array}{l} 2x+3y= -10①,\\ 3x-5y= -6②,\end{array} \right. $下列做法正确的是(C)
A.要消去y,可以将$\enclose{circle} {1}×5+\enclose{circle} {2}×2$
B.要消去x,可以将$\enclose{circle} {1}×5+\enclose{circle} {2}×2$
C.要消去y,可以将$\enclose{circle} {1}×5+\enclose{circle} {2}×3$
D.要消去x,可以将$\enclose{circle} {1}×(-5)+\enclose{circle} {2}×2$

答案： C

4. 已知关于x,y的方程组$\left\{\begin{array}{l} mx+2y= n,\\ 4x-ny= 2m-1\end{array} \right. 的解是\left\{\begin{array}{l} x= 1,\\ y= -1,\end{array} \right. $那么m,n的值为(D)
A.$\left\{\begin{array}{l} m= 1,\\ n= -1\end{array} \right. $
B.$\left\{\begin{array}{l} m= 2,\\ n= 1\end{array} \right. $
C.$\left\{\begin{array}{l} m= 3,\\ n= 2\end{array} \right. $
D.$\left\{\begin{array}{l} m= 3,\\ n= 1\end{array} \right. $

答案： D

5. 若方程组$\left\{\begin{array}{l} x-by+4z= 1,\\ x-2by+3z= 3\end{array} \right. 的解是\left\{\begin{array}{l} x= a,\\ y= 1,\\ z= c,\end{array} \right. 则a+b+6c$的值是(A)
A.-3
B.0
C.3
D.6

答案： A

6. 小明求得二元一次方程组$\left\{\begin{array}{l} 4x+y= 12,\\ 3x-2y= ■\end{array} ■ \right. 的解为\left\{\begin{array}{l} x= ●,\\ y= 4,\end{array} \right. $由于不小心,滴上了墨水,刚好遮住了两个数●和■,则这两个数分别为(D)
A.-2和2
B.-2和4
C.2和-4
D.2和-2

答案： D

7. 我国古代数学著作《孙子算经》中有“鸡兔同笼”问题:“今有鸡兔同笼,上有16头,下有44足,问鸡兔各几何.”设鸡x只,兔y只,则可列方程组为(A)
A.$\left\{\begin{array}{l} x+y= 16,\\ 2x+4y= 44\end{array} \right. $
B.$\left\{\begin{array}{l} x+y= 16,\\ 2x+2y= 44\end{array} \right. $
C.$\left\{\begin{array}{l} x+y= 16,\\ 4x+4y= 44\end{array} \right. $
D.$\left\{\begin{array}{l} x+y= 16,\\ 4x+2y= 44\end{array} \right. $

答案： A

8. 已知$3x^{|m|}+(m+1)y= 6$是关于x,y的二元一次方程,则m的值为____1.

答案： 1

9. 已知$\left\{\begin{array}{l} x= -2,\\ y= 3\end{array} \right. $是关于x,y的方程组$\left\{\begin{array}{l} 3x-2ay= 6,\\ b+4y= -2\end{array} \right. $的解,则关于x的方程$ax+b= 1$的解是____$-\frac{15}{2}$.

答案： $-\frac{15}{2}$

10. 已知方程组$\left\{\begin{array}{l} 2x+y= 3,\\ 2y+2z= 4,\\ z+x= 5,\end{array} \right. 则x+y+z$的值为____4.

答案： 4

11. 在关于x,y的方程组$\left\{\begin{array}{l} x-y= 4,\\ 2x= m-3y\end{array} \right. $中,若$x= 6$,则$m= $__18__

答案： 18

12. 对于任意有理数a,b,c,d,规定$\begin{vmatrix} a&b\\ c&d\end{vmatrix} = ad-bc$.已知x,y同时满足$\begin{vmatrix} x&y\\ -1&4\end{vmatrix} = 5,$$\begin{vmatrix} 5&y\\ -3&x\end{vmatrix} = 1$,则$x+y= $-1.

答案： -1