For the question:
Given that the determinant of the 3x3 matrix of (left to right, top to bottom) (a, 1, 1)(b, 2, 1)(c, 3, 1) is -9, find the exact value of x when ax+y+z=1,bx+2y+z=-2 and cx+3y+z=3.
I've already figured out from the matrix that -a+2b-c=-9, what should I do now?

Question

For the question:
Given that the determinant of the 3x3 matrix of (left to right, top to bottom) (a, 1, 1)(b, 2, 1)(c, 3, 1) is -9, find the exact value of x when ax+y+z=1,bx+2y+z=-2 and cx+3y+z=3.
I've already figured out from the matrix that -a+2b-c=-9, what should I do now?

clarence · Answer

$$\left[\begin{matrix}a & 1 & 1 \ b & 2 & 1 \ c & 3 & 1\end{matrix}\right]$$

clarence · Answer

I think I've worked it out, isn't it just 8/9?

mathmate · Answer

Yes, 8/9 is correct for x.  Cramer's rule?

clarence · Answer

Yup, seemed like the only way to work out the question, thanks for the confirmation!

mathmate · Answer

You're welcome!  :)