《2025年七彩假期暑假作业七年级数学》

1. 二元一次方程组$\left\{\begin{array}{l} x+y= 3,\\ 2x= 4\end{array} \right. $的解是 (D)

A.$\left\{\begin{array}{l} x= 3,\\ y= 0\end{array} \right. $
B.$\left\{\begin{array}{l} x= 1,\\ y= 2\end{array} \right. $
C.$\left\{\begin{array}{l} x= 5,\\ y= -2\end{array} \right. $
D.$\left\{\begin{array}{l} x= 2,\\ y= 1\end{array} \right. $

答案： D

2. 已知方程组$\left\{\begin{array}{l} 5x+y= 3,\\ ax+5y= 4\end{array} \right. 和\left\{\begin{array}{l} x-2y= 5,\\ 5x+by= 1\end{array} \right. $有相同的解,则$a、b$的值为 (A)

A.$\left\{\begin{array}{l} a= 14,\\ b= 2\end{array} \right. $
B.$\left\{\begin{array}{l} a= 4,\\ b= -6\end{array} \right. $
C.$\left\{\begin{array}{l} a= -6,\\ b= 2\end{array} \right. $
D.$\left\{\begin{array}{l} a= 1,\\ b= 2\end{array} \right. $

答案： A

3. 已知$|x+y+1|+(x-y+3)^{2}= 0$,则$(x+y)^{2019}= $ (B)

A.$2^{2019}$
B.$-1$
C.$1$
D.$-2^{2019}$

答案： B

4. 方程组$\left\{\begin{array}{l} x-y= 4,\\ 2x+y= -1\end{array} \right. $的解是 $\left\{\begin{array}{l} x=1,\\ y=-3\end{array}\right. $.

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

5. 如果实数$x、y满足方程组\left\{\begin{array}{l} 2x-2y= 1,\\ x+y= 4,\end{array} \right. 那么x^{2}-y^{2}= $2.

答案： 2

6. (夹江县二模)解方程组:$\left\{\begin{array}{l} 2x-y= 5,\\ x-1= \frac {1}{2}(2y-1).\end{array} \right. $

答案： 方程组的解为$\left\{\begin{array}{l} x=\frac {9}{2},\\ y=4.\end{array}\right. $

7. 已知关于$x、y的方程组\left\{\begin{array}{l} 3x-y= 5,\\ 4ax+5by= -22\end{array} \right. 与\left\{\begin{array}{l} 2x-3y+4= 0,\\ ax-by-8= 0\end{array} \right. $有相同的解,求$a、b$的值.

答案： 解:根据题意得$\left\{\begin{array}{l} 3x-y=5,\\ 2x-3y+4=0,\end{array}\right. $解得$\left\{\begin{array}{l} x=\frac {19}{7},\\ y=\frac {22}{7}.\end{array}\right. $代入其他两个方程,可得方程组为$\left\{\begin{array}{l} \frac {76}{7}a+\frac {110}{7}b=-22,\\ \frac {19}{7}a-\frac {22}{7}b-8=0,\end{array}\right. $解得$\left\{\begin{array}{l} a=\frac {14}{19},\\ b=-\frac {21}{11}.\end{array}\right. $