Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations

No solution I might be wrong  can someone confirm?

a+2b+3c+4d+5e=41

2a+3b+4c+5d+e=15

3a+4b+5c+d+2e=34

4a+5b+c+2d+3e=63

5a+b+2c+3d+4e=57

Use eliminations ans substitutions to get:

a = 6,  b = 4,  c = - 3,  d = - 1,  e = 8

This solution balances the 5 equations.