Sysmtem of equations with a variable

[MerijnThijs]

So, I really got stuck at the following problem and I hope one of you might be able to help me

I now have the value's of a, a =1 and a = -6 by making it a matrix and setting the det to 0. I checked these value's and they are correct. Now I can't figure out how to solve x, y and z. please help
These are the solutions:

 

[Deleted member 4993]

So, I really got stuck at the following problem and I hope one of you might be able to help me
View attachment 22108
I now have the value's of a, a =1 and a = -6 by making it a matrix and setting the det to 0. I checked these value's and they are correct. Now I can't figure out how to solve x, y and z. please help
These are the solutions:
View attachment 22109

Did you replace \(\displaystyle \alpha\ \) by 1, in the given equations and try to solve for x. y and z?

What did you get?

Please show detailed work.