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Homework Statement
Find all the values of h and k such that the system:
hx + 6y = 2
x + (h+1)y = k
has: (a) No solutions (b) A unique solution (c) Infinitely many solutions
Homework Equations

The Attempt at a Solution
I've tried putting the system into echelon form and got the following (with the augmented matrix):
(1 h + 1 k)
(0 h^{2}+h6 hk2)
However, how can i proceed from this step? Note that the only way i can solve this problem is using matrices, i've got the answer by comparing the linear systems but i need to do it with matrices.