Question: What's wrong with this argument: These three show that if a homogeneous system has one solution then it has many solutions-any multiple of a solution

What's wrong with this argument: "These three show that if a homogeneous system has one solution then it has many solutions-any multiple of a solution is another solution, and any sum of solutions is a solution also-so there are no homogeneous systems with exactly one solution."?

s and t (a) s+t (b3 (c) ks+mt for k, m R

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