Solving linear equations with exactly one solution

[baki]

1.Determine the value(s) of k for which the system of linear equations
x + 2y = 1
(k²)x - 2ky = 2
has exactly one solution 3.How do i solve this, i tried the 2x2 matrix
whereby, i had
|1 2|
|k² -2k|
and tried to make [2 and k^2 = zero] and [-2k = one]
But I can't seem to solve it completely
is there another way we can do this?

 

[LCKurtz]

This is a duplicate post of https://www.physicsforums.com/showthread.php?t=651710

 

[SammyS]

[ b]1.Determine the value(s) of k for which the system of linear equations
x + 2y = 1
(k²)x - 2ky = 2
has exactly one solution [/b]

[ b]3.How do i solve this, i tried the 2x2 matrix
whereby, i had
|1 2|
|k² -2k|
and tried to make [2 and k^2 = zero] and [-2k = one]
But I can't seem to solve it completely
is there another way we can do this?
[/b]

Try solving the system, as it is, for x & y.

See how k is involved in that solution.

 

[baki]

I've tried that and there are 2 values of k, but don't you think when it says it has exactly one solution than it means k should have one value.

 

[SammyS]

I've tried that and there are 2 values of k, but don't you think when it says it has exactly one solution than it means k should have one value.

No.

It means, "What value or values may k have so that the system has one (x, y) solution?"