SOLUTION: Determine the values ​​of K for which the following system has a nonzero solution:
Kx + Ky = 0 4x + 2Ky = 0
The official answer is K=0 and K=2 but I don't know
Algebra.Com
Question 549766: Determine the values of K for which the following system has a nonzero solution:
Kx + Ky = 0 4x + 2Ky = 0
The official answer is K=0 and K=2 but I don't know how to do this. Help me please!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have worded the question incorrectly because if 
or 
then the given system is either consistent/dependent (same line) or inconsistent (parallel lines).
Calculate the determinant:
If the determinant is zero, then the system is either consistent/dependent (same line) or inconsistent (parallel lines).
or
So or yields no unique solution.
In fact, the set of values of 
for which your system yields a unique solution is all real numbers EXCEPT 0 and 2. Note, however, that the unique solution is, in every case, the origin )
John
My calculator said it, I believe it, that settles it
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