Use the following system of equations: x-2y=1 x-y+kz=-2 ky+4z=6 The value(s) of

Question

Use the following system of equations:

x-2y=1

x-y+kz=-2

ky+4z=6

The value(s) of k such that the system has a unique solution is (are)?

The value(s) of k such that the system has infinitely many solutions is (are)?

We reviewed seveal methods i.e. row echelon and Gaussian elimination with back substitution in class. I have attempted to apply them, but must be doing something wrong as it is not that often that we have answers of "none of the above", so I sincerely doubt I would have two in a row.

Any assistance with clear, detailed steps and explanation will be greatly appreciated!!! THANKS!

Explanation / Answer

1. If the twoequationshappen to be the same, then you got one uniqueequationfor two variables. This results in infinite solution. In this case, it happens if

4x + ky = 6 is the same as kx + y = -3 or -2kx - 2y = 6

For coefficients of x: 4 = -2k ==> k = -2
For coefficients of y: k = -2.

Therefore, when k = -2, both equations are the same as 2x - y = 3 and have infinite solutions.

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