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A question about linear equations
Posted:
Jun 21, 2013 8:57 PM


Question:Show that if the linear equations x1+k*x2=c and x1+l*x2=d have the same solution set, then the two equations are identical.(i.e. k=l and c=d)
My answer. for equation 1: x1=ck*x2, let x2=t (t is a parameter), then x1=ck*t for equation 2: x1=dl*x2, let x2=t, then x1=dl*t. if x1 and x2 are solutions for both equations 1 and 2,then ck*x2=dl*x2, and then here my question comes for I can find two situations,
1.c=d and k=l 2.c=3 d=4,k=2,and l=3,then x1=1 and x2=1 for equations 1 and 2.
That means even though c doesn't equal to d and k doesn't equal to l, these two equations still get the same solution set. Then how to prove it?
Or, did I do something wrong?
Thanks.



