Question 1121327
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If you know what a determinant of a matrix is (if you just learned it), then you can calculate the determinant of the coefficient matrix


    det {{{(matrix(2,2, 9,k, k,1))}}} = 9*1 - k*k = 9 - k^2.


The system has no solutions or infinitely many solutions if and only if the determinant is equal to zero


    9 - k^2 = 0  ====>  k^2 = 9  ====>  k = +/- 3.


For all other values of "k", different from 3 or -3, the system has a unique solution.
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