《2025年时习之暑假衔接七年级数学人教版》

4. 若$(a-3)x+y^{|a|-2}= 9$是关于x,y的二元一次方程,则a的值为____.

答案： -3

5. 已知$\left\{\begin{array}{l} x= 2,\\ y= -1\end{array} \right. 是二元一次方程ax+by= 2$的一组解,则$4-2a+b= $____.

答案： 2

6. 二元一次方程组$\left\{\begin{array}{l} x+y= 3,\\ x-y= -1\end{array} \right. $的解是( )

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： B

7. 用代入法解方程组$\left\{\begin{array}{l} y= 2x-3\textcircled{1},\\ 3x+2y= 8\textcircled{2}\end{array} \right. $时,将方程①代入②中,所得的方程正确的是( )

A.$3x+4x-3= 8$
B.$3x+4x-6= 8$
C.$3x-2x-3= 8$
D.$3x+2x-6= 8$

答案： B

8. 已知$\left\{\begin{array}{l} x-y= 3,\\ x+3y= -5,\end{array} \right. 则x+y$的值是( )

A.3
B.1
C.-3
D.-1

答案： D

9. 已知$(x-y+3)^{2}+\sqrt {2x+y}= 0$,则x,y的值分别为( )

A.-1,2
B.1,-2
C.-1,-2
D.1,2

答案： A

10. 关于x,y的二元一次方程$3x-y= 4$,用含x的代数式表示y,则$y= $____.

答案： $3x-4$

11. 如果$\frac {1}{2}a^{3x}b^{y}与-a^{2y}b^{x+1}$是同类项,那么x,y的值分别为____.

答案： 2,3

12. 已知$\left\{\begin{array}{l} x= 2,\\ y= 1\end{array} \right. 是二元一次方程组\left\{\begin{array}{l} mx+ny= 7,\\ nx-my= 1\end{array} \right. $的解,则$m+3n$的立方根为____.

答案： 2

13. 解下列方程组：
(1)$\left\{\begin{array}{l} y= 2x-3,\\ 5x+y= 11;\end{array} \right. $
(2)$\left\{\begin{array}{l} 3x-y= 7,\\ x+3y= -1;\end{array} \right. $
(3)$\left\{\begin{array}{l} 3x-5y= 3,\\ \frac {x}{2}-\frac {y}{3}= 1.\end{array} \right. $

答案：
(1)$\left\{\begin{array}{l} x=2,\\ y=1.\end{array}\right. $
(2)$\left\{\begin{array}{l} x=2,\\ y=-1.\end{array}\right. $
(3)$\left\{\begin{array}{l} x=\frac {8}{3},\\ y=1.\end{array}\right. $

14. 已知$\left\{\begin{array}{l} x= 2,\\ y= 3\end{array} \right. 和\left\{\begin{array}{l} x= -4,\\ y= 2\end{array} \right. $是关于x,y的二元一次方程$2ax-by= 2$的两组解,求a,b的值.

答案： 把$\left\{\begin{array}{l} x=2,\\ y=3\end{array}\right. $和$\left\{\begin{array}{l} x=-4,\\ y=2\end{array}\right. $分别代入$2ax-by=2$可得$\left\{\begin{array}{l} 4a-3b=2,\\ -8a-2b=2,\end{array}\right. $解得$\left\{\begin{array}{l} a=-\frac {1}{16},\\ b=-\frac {3}{4}.\end{array}\right. $