1.
(2023八上·兴宁开学考)
“整体思想”是数学解题中的一种重要的思想方法.数学课上,李老师给出了一个问题,已知实数x , y满足
, 求x-4y和7x+5y的值.
小天:利用消元法解方程组,得x , y的值后,再代入求x-4y和7x+5y的值;
小红:发现两个方程相同未知数系数之间的关系,通过适当变形,整体求得代数式的值,3x-y=5①,2x+3y=7②,由①-②可得x-4y=-2,由①+②×2可得7x+5y=19;
李老师对两位同学的讲解进行点评,指出小红同学的思路体现了数学中“整体思想”的运用.请你参考小红同学的做法,解决下面的问题:
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(1)
已知二元一次方程组
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 则
x-
y=
,
x+
y=
;
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(2)
请说明在关于
x ,
y的方程组
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%7B%3C%2Fmo%3E%3Cmtable+columnalign%3D%22left%22%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3Cmtr%3E%3Cmtd%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmi%3Ey%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmtd%3E%3C%2Fmtr%3E%3C%2Fmtable%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
中,无论
a为何值,
x+
y的值始终不变;
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(3)
八年级(1)班开展安全教育知识竞赛需购买奖品,若买3支铅笔、5块橡皮、1本笔记本共需21元;若买4支铅笔、7块橡皮、1本笔记本共需28元,则购买10支铅笔、10块橡皮、10本笔记本共需多少元?(直接写出结果)
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