Use the following system of equations: x-2y=1 x-y+kz=-2 ky+4z=6 The value(s) of
ID: 2982907 • Letter: U
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.