Question 1101074
original
1 1 0 24
0 1 1 21
1 0 1 27
determinant =2
inverse matrix fractional form
1/2 -1/2 1/2
1/2 1/2 -1/2
-1/2 1/2 1/2

24 21 27

solutions and sum
15 + 9 + 12 =36
The process is much too long to present here.
I can only assume that such a problem was given to practice the inverse matrix method so that you could check your result easily with ankor's method..
There are several inverse matrix methods including using gauss jordan, using the identity matrix and using determinants, cofactors and and adjoint.
I used determinant, cofactor and and adjoint.

Ankor's method didn't need to find a,b and c individually.

Yesterday, Ikleyn used a similar method as Ankor to solve the same problem stating it is the most obvious and simplest choice to solve this problem. It is but I suppose that the teacher is introducing inverse matrix method and started with an easy system of equations