Question 1127260
This is not taken to completion:


{{{(matrix(3,4,1,1,-1,0,1,-1,1,c-b,1,-1,-1,a-c))}}}


process,
--
E1-E2;
E2-E3;
from that result, 
E2+E3;
returning again to the original matrix,
E1+E2:


{{{(matrix(2,4,2,0,0,c-b,0,3,0,-a-c))}}}


This means  {{{system(x=(c-b)/2,y=-(a+c)/3)}}}
Not yet finished, and not yet fully checked.
Other possible methods.