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=7Â implies
u+v=7
2/x+3/y=17Â 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