AN EASY QUESTION

a1x1+b1=a2x2+b2.
find x1,x2 which statisfy the given equation such that x1+x2 is minimum.given (a1,a2,b1,b2).
i am able to solve the given problem but it is taking too much time and my solution is also not satisfying me.cam someone provide me with a short and apt solution for dis problem…Thanks…

a1x1+b1=a1x2+b2.

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Rewriting the above equation:

x1=(a2/a1)x2+(b2-b1)/a1

Since a1,b1,a2,b2 are constants,let a2/a1=m and (b2-b1)/a1=n

then the equation becomes x1=m*x2+n

So, S=x1+x2=(m+1)*x2+n

So S is minimum when x2 is minimum.

So,the answer is the Pair < m*x2+n , x2 >

If x1,x2>0 then the ans is < m+n , 1 >

So, S=x1+x2=(m+1)*x2+n… i am confused with this step… can i know how this satisfy this condition.??

x1 = mx2 + n
and
S = x1 + x2
S = m
x2 + n + x2 (Substituting x1 with m*x2 + n)
S = (m+1)*x2 + n

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