Math CentralQuandaries & Queries


Question from smithu, a student:

x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method, cross multiplication, substitution method


The first observation is that a can't be zero and b can't be zero.

Multiply both sides of x/a + y/b = a+b by ab and multiply both sides of x/a2 + y/b2 = 2 by a2 b2. This will give you two equations which you can solve using the elimination method. When I did this I cancelled a factor of (a - b) and hence this procedure fails if a = b. At this point you need to go back to the original equations and rewrite them with a = b. The two equations then collapse to one equation and any choices of x and y that satisfy this equation gives additional solutions.


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