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 1/x+1/y=7, 2/x+3/y=17 and we have to find the value of variables x and y from the given equations by using the method of cross multiplication

RS Aggarwal, Class 10, chapter 3C, question no 9

Simplify given equations:

Let 1/x=u and 1/y=v

1/x+1/y=7 implies

u+v=7

2/x+3/y=17 implies

2u+3v=17

New set of equation is:

u+v=7...(1)

2u+3v=17...(2)

From equation (1):a1=1,b1=1 and c1=−7

From equation (2):a2=2,b2=3 and c2=−17

Using cross multiplication method:

u/(−17+21)=v/(−14+17)=1/(3−2)

u/4=1 and v/3=1

u=4 and q=3

x=1/4 nad y=1/3 [Since we consider p=1/x and q=1/y]

Answer x=1/4,y=1/3