Question 1068184: For a certain value of k, the system:
x + y + 3z = 10
-4x + 2y + 5z = 7
kx + z = 3
has no solutions. What is this value of k? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! USING DETERMINANTS:
Of you have learned about using matrices and determinants
to solve systems of equations,
you would know that the matrix associated with that system is ,
and that the system has no solution if the determinant for that matrix is zero: <--> <--> <--> .
WITHOUT DETERMINANTS:
One way to solve that system would be
to make a linear combination of the first two equations that would have no term with ,
and then try to solve the system made from the resulting equation and
Adding the first equation times
plus the second one times , we get .
Then you would solve the system
Obviously, if ,
that system (and the original system)
Would have no solution.
