MHB Find the value of k for the following system to have no solutions etc?

[orgekas]

Find the values of k , if any, for which the following system of equations has
i) no solutions,
ii) infinitely many solutions
and
iii) a unique solution. Solve and find the unique solution.

(k+1)*(X₁) + 3*(X₂) - (X₃) =22

2*(X₁) + K*(X₂) + (X₃) =14

(X₁) + 4*(X₂) + (X₃) =20

 

[I like Serena]

Hi orgekas! Welcome to MHB! (Smile)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[orgekas]

Ok. I solved it now I don't any help. Thanks I'll include my working out in my future posts.
Thank you.