《2025年轻松总复习暑假作业七年级数学》

17. 解下列方程组:
(1)$\left\{\begin{array}{l} x-2= 2(y-1),\\ 2(x-2)+y-1= 5;\end{array} \right. $
(2)$\left\{\begin{array}{l} \frac {x+2y}{6}= 1,\\ \frac {x-y}{3}= 1.\end{array} \right. $

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

18. 解下列不等式(组),并把解集在数轴上表示出来.
(1)$1+\frac {x-1}{3}≤\frac {2x+3}{3}-x;$
(2)$\left\{\begin{array}{l} 3x+2＞2x-3,\\ \frac {2x-1}{3}＜1.\end{array} \right. $

答案：
(1)$x≤\frac {1}{2}$,数轴表示略.
(2)$-5\lt x＜2$,数轴表示略.

19. 如图所示,已知$AB// CD$,且AE平分$∠BAD$,DF平分$∠ADC$,请说明:$AE// DF.$

答案： 解:$\because AB// CD,\therefore ∠BAD=∠CDA.$
$\because ∠1=\frac {1}{2}∠BAD,∠2=\frac {1}{2}∠ADC,\therefore ∠1=∠2,$
$\therefore AE// DF.$