If h is preferred as -2, the two equations would be 6 x - 3 y = -2 and also -12 x + 6 y = 4. The second of these is -2 times the first. ( Explicitly reflecting that they are not independent.) So, with h = -2, tright here are infinitely many kind of services (x,y) all through y = 2 x + 2/3. Consistent but degenerate.

You are watching: Determine the value of h such that the matrix is the augmented matrix of a consistent linear system

For any type of other option of h, the 2 equations have actually no services because they correspond to parallel lines. This would be thought about an inconsistent straight system.

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