《2025年时习之暑假衔接七年级数学人教版》

1. 下列方程中,是二元一次方程的是( )

A.$\frac {5}{m}-2n= 12$
B.$\frac {7}{4}y-\frac {11}{6}z= -a$
C.$y= 3x-2$
D.$mn+m= 7$

答案： C

2. 已知方程组$\left\{\begin{array}{l} 3x+2y= 7\textcircled{1},\\ 4x-y= 13\textcircled{2},\end{array} \right. $下列变形正确的是( )

A.①×2-②消去x
B.①-②×2消去y
C.①×2+②消去x
D.①+②×2消去y

答案： D

3. 已知x,y满足关系式$2x+y= 9和x+2y= 6$,则$x+y$的值为( )

A.6
B.-1
C.15
D.5

答案： D

4. 已知$\left\{\begin{array}{l} x= 0,\\ y= -1\end{array} \right. 是方程组\left\{\begin{array}{l} x-b= y,\\ 5x+2a= 2y\end{array} \right. $的解,则ab等于( )

A.-1
B.0
C.1
D.2

答案： A

5. 若$|x+y+1|与(x-y-2)^{2}$互为相反数,则$(3x-y)^{3}$的值为( )

A.1
B.9
C.-9
D.27

答案： D

6. 已知方程$5x-2y= 7$,用含x的代数式表示y,则$y= $____.

答案： $\frac {5}{2}x-\frac {7}{2}$

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

答案： $\left\{\begin{array}{l} x=3,\\ y=2\end{array}\right. $

8. 以方程组$\left\{\begin{array}{l} y= -x+2,\\ y= x\end{array} \right. 的解为坐标的点(x,y)$在第____象限.

答案： 一

9. 已知$\left\{\begin{array}{l} x= 4,\\ y= -2\end{array} \right. 与\left\{\begin{array}{l} x= -2,\\ y= -5\end{array} \right. 都是方程y= ax+b$的解,则$\sqrt {a^{2}-3b}= $____.

答案： $\frac {7}{2}$

10. 解下列方程组：
(1)$\left\{\begin{array}{l} x= 2y,\\ 2x-3y= 2;\end{array} \right. $
(2)$\left\{\begin{array}{l} 3x+y= 7,\\ 2x-y= 3;\end{array} \right. $
(3)$\left\{\begin{array}{l} 3x+2= 5y,\\ \frac {2x-3}{2}+y= \frac {17}{2};\end{array} \right. $
(4)$\left\{\begin{array}{l} x+y+z= 1,\\ x-2y-z= 3,\\ 2x-y+z= 0.\end{array} \right. $

答案：
(1)$\left\{\begin{array}{l} x=4,\\ y=2.\end{array}\right. $
(2)$\left\{\begin{array}{l} x=2,\\ y=1.\end{array}\right. $
(3)$\left\{\begin{array}{l} x=6,\\ y=4.\end{array}\right. $
(4)$\left\{\begin{array}{l} x=3,\\ y=2,\\ z=-4.\end{array}\right. $

11. 若方程组$\left\{\begin{array}{l} 3x+4y= 2,\\ 2x-y= 5\end{array} \right. 与方程组\left\{\begin{array}{l} \frac {a}{3}x-by= 4,\\ ax+\frac {b}{2}y= 5\end{array} \right. $有相同的解,求a,b的值.

答案： 解方程组$\left\{\begin{array}{l} 3x+4y=2,\\ 2x-y=5,\end{array}\right. $得$\left\{\begin{array}{l} x=2,\\ y=-1.\end{array}\right. $将$\left\{\begin{array}{l} x=2,\\ y=-1\end{array}\right. $代入方程组$\left\{\begin{array}{l} \frac {a}{3}x-by=4,\\ ax+\frac {b}{2}y=5\end{array}\right. $中,得$\left\{\begin{array}{l} \frac {2}{3}a+b=4,\\ 2a-\frac {b}{2}=5,\end{array}\right. $解得$\left\{\begin{array}{l} a=3,\\ b=2.\end{array}\right. $