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Ray Vickson
#6
Mar9-12, 09:06 AM
Sci Advisor
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Quote Quote by imiyakawa View Post
1. The problem statement, all variables and given/known data
If;
a*x + b*y = c*x + d*y
x ≠ y
a,b,c,d ≥ 0

Prove that;
a=c
b=d

2. The attempt at a solution
I've been fiddling with this equation and have been getting nowhere.
It is not true. For example, the equation 2*x + y = x + 3*y has many solutions, all of the form x = 2*y; the solution satisfies x ≠ y as long as x ≠ 0.

On the other hand, if you really mean that a*x + b*y = c*x + d*y should be true for ALL x ≠ y, then the result is true.

RGV