Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a+2b+3c+4d+5e=47,2a+3b+4c+5d+e=15,3a+4b+5c+d+2e=3,4a+5b+c+2d+3e=26,5a+b+2c+3d+4e=29.
I found the answer: (a,b,c,d,e) = (4,2,-3,-1,8).