SOLUTION: find all the value/s of k so that the system x+y=2 and x+(k^2 -3)y=k has
a) no solution
b) infinitely many solutions
c) a unique solution
Algebra.Com
Question 767070: find all the value/s of k so that the system x+y=2 and x+(k^2 -3)y=k has
a) no solution
b) infinitely many solutions
c) a unique solution
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
In order for there to be no solution, the ratio of the coefficient on 
to the coefficient on 
in one of the equations has to be the same as the same ratio for the other equation AND the constant terms in the two equations must be different.
So, since the coefficients on and are 1 and 1 in the first equation, the coefficients on and must be in the ratio 1 to 1 in the second equation. Therefore 
.
Solving the quadratic, 
For no solution, 
For infinite solutions, 
For a unique solution, 
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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