Sir please give me a detailed solution of this question as it was already asked in various important examinations in which we have given two equations 5/(x+y)-2/(x-y)+1=0, 15/(x+y)+7/(x-y)-10=0 and we have been asked to find the value of variables x and y by using the method of cross multiplication
RS Aggarwal, Class 10, chapter 3C, question no 10
Substitute 1/(x+y)=a and 1/(x−y)=b
We get equations as follows: 5a−2b+1=0 and 15a+7b−10=0
Using method of cross-multiplication we get:
a/(−2)(−10)−(7)(1)=b/(1)(15)−(−10)(5)=1/(5)(7)−(15)(−2)
a/13=b/65=1/65
From a/13=1/65 we get a=1/5
Similarly b=1
Resubstituting values of a and b we get x+y=5 and x−y=1
Adding these 2 equations gives us x=3 .
Substracting 2nd equation from 1st gives us y=2