Question 996561
.
If you know 


1)  what is the determinant of a linear system of two equations with two unknowns  (or what is the determinant of a  2x2 matrix),  and


2)  if you know how the determinant is connected with a solution of a linear system of two equations in two unknowns  (Cramer's rule)


then your condition for  k  is non-vanishing the determinant.  In other words,  the solution does exist and is unique if the determinant is not zero.


In your case it will give you a quadratic equation for  k.


If you don't know it and want to expand your knowledge,  read the lesson


<A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-two-unknowns-using-Cramer%27s-rule.lesson>Solving systems of linear equations in two unknowns using the Cramer's rule</A>


in this site. &nbsp;Look also in the lessons that are under the links in this lesson.


It is free of charge and without registration.


Thanks for asking.