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Question 996561: I've been trying to figure this question:
Find conditions on k that will make the following system of equations have a unique solution. Then give a formula in terms of k for the solution to the system, when it exists.
3kx+18ky = 4
x+3ky = 4
I feel as if I should know this but I'm not getting anywhere. Any help would be appreciated.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
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
Solving systems of linear equations in two unknowns using the Cramer's rule
in this site. Look also in the lessons that are under the links in this lesson.
It is free of charge and without registration.
Thanks for asking.
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