《2025年假期园地暑假作业七年级数学人教版》

7. 解下列方程组:
(1)$\left\{\begin{array}{l} \frac {x-y}{2}-1= \frac {2x+y}{2},\\ \frac {3x+y}{3}+2= \frac {x-y}{3};\end{array} \right. $
(2)$\left\{\begin{array}{l} 0.5x+0.7y= 35,\\ x+0.4y= 40.\end{array} \right. $

答案： （1）解方程组$\left\{\begin{array}{l} \frac {x-y}{2}-1=\frac {2x+y}{2},①\\ \frac {3x+y}{3}+2=\frac {x-y}{3}.②\end{array}\right. $化简为$\left\{\begin{array}{l} -x-2y=2,\\ x+y=-3.\end{array}\right. $解得$\left\{\begin{array}{l} x=-4,\\ y=1.\end{array}\right. $（2）化简,得$\left\{\begin{array}{l} 5x+7y=350,③\\ 5x+2y=200.\enclose{circle} {4}\end{array}\right. $③-④得$5y=150,y=30.$将$y=30$代入③,得$x=28$.
∴原方程组的解为$\left\{\begin{array}{l} x=28,\\ y=30.\end{array}\right. $

8. 李华在玩具厂做工,做4只小狗和7辆汽车用去3小时42分,做5只小狗和6辆汽车用去3小时37分,求做14只小狗和19辆汽车用多少时间.

答案： 解：设做1只小狗用x分，做1辆汽车用y分，由题意得$\left\{\begin{array}{l} 4x+7y=3×60+42,①\\ 5x+6y=3×60+37.②\end{array}\right. $②×2+①得$14x+19y=656.$656(分)=10(时)56(分).答:做14只小狗、19辆汽车用10小时56分.