Question 1101027
original
a + b = 24   
b + c = 21    
a + c = 27   
matrix
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 suppose that the teacher is introducing inverse matrix method and started with an easy system of equations. I can only assume that such a problem was given to practice the inverse matrix method so that you could check your results easily with Ikleyn's method.

Ikleyn is correct in saying that her method is THE STANDARD METHOD  for solving problems like this.

There are several inverse matrix methods including using gauss jordan, identity matrix and using determinants, cofactors and and adjoint.

I used determinant, cofactor and adjoint.