Question

How do I go about solving this system without using matrices? K can be does not exist, is equal to, or does not equal to

Answer 1

(-∞, 29/7) ∪ (29/7, ∞)

Explanation:

The only value of k that will make the system have something other than one solution is the value that puts it in the same proportion as the coefficients in the first equation.

3/21 ≠ k/29

k ≠ 29/7 . . . . . . multiply by 29 and simplify

So, "all values of k" will be ...

(-∞, 29/7) ∪ (29/7, ∞)