Question

How to find k to make this system consistent?

How to find k to make this system consistent?

Answer 1

System is consistent if `k!=-7`

Explanation:

For three linear simultaneous equations in three variables to have a consistent solution, we must have `Delta!=0`, where `Delta` is the discriminant of the matrix of the coefficients of the variables i.e. `x,y` and `z`. Here we should have

`|(-3,-6,6),(9,8,k),(-45,-50,46)|!=0`

or `-3*(8*46-k(-50))-6*(k*(-45)-9*46)+6(9*(-50)-8*(-45))!=0`

i.e. `-3(368+50k)-6(-45k-414)+6(-450+360)!=0`

or `-1104-150k+270k+2484-2700+2160!=0`

or `120k+840!=0`

or `k!=-7`