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笔者在人教版七年级第二章的配套练习题中,发现这样一道例题:已知x+4y=-1,xy=5,求(6xy+7y)+[8x-(5xy-y+6x)]的值.分析此类试题,当字母的具体数字没有给出,且又不易求出时,求代数式的值常用两种方法:(1)分析已知条件和所求的问题,观察所求的代数式中是否能化简并构造出已知条件的形式,采用整体代换:(2)将其中一个字母用另一个字母表示,代入所求的式子中,达到消元的目的,即解法一:(6xy+7y)+[8x-(5xy-y+6x)]=6xy+7y+[8x-5xy+y-6x]=6xy+7y+8x-5xy+y-6x=xy+2x+8y=xy+2(x+4y)
In the seventh edition of the PEP, I found the following example: we know that x + 4y = -1 and xy = 5, and we find that 6xy + 7y + 8x- (5xy-y + 6x ) Analysis of such questions, when the alphabetic specific figures are not given, and not easy to find algebraic value commonly used in two ways: (1) analysis of known conditions and the requirements of the problem, Seeking algebraic formula can simplify and construct the form of known conditions, the use of the overall substitution: (2) one of the letters with another letter, substituted into the desired formula, to eliminate the purpose of Solution 1: 6xy + 7y + 8x- 5xy-y + 6x = 6xy + 7y + 8x-5xy + y- 8y = xy + 2 (x + 4y)