Although you should do your homework yourself I think I can help you : )
This problem could be solved with the backslash operator (or mldivide)
X = [1 1 1
-2 2 1
1 1 -2]; % These are the coefficients from your linear system
Y = [4
6
6]; % these are the responses from your linear system
P = X\Y; % and P' would be your [x1,x2,x3]
