Need help with system
Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 41
2a + 3b + 4c + 5d + e = 15
3a + 4b + 5c + 1d + 2e = 34
4a + 5b + 1c + 2d + 3e = 68
5a + 1b + 2c + 3d + 4e = 57
a + 2b + 3c + 4d + 5e = 41..........(1)
2a + 3b + 4c + 5d + e = 15..........(2)
3a + 4b + 5c + 1d + 2e = 34........(3)
4a + 5b + 1c + 2d + 3e = 68........(4)
5a + 1b + 2c + 3d + 4e = 57........(5)
Add the 5 equations together:
15a + 15b + 15c + 15d + 15e=215
Divide both sides by 15:
a + b + c + d + e ==43 / 3...............(6)
Subtract (1) from (2) above:
a + b + c + d -4e == - 26...................(7)
Subtract (7) from (6) above:
5e ==121 / 3
e ==121 / 15 sub this for e in (2) and (3) and (6) above:
Subtract (2) from (3) above:
a + b + c - 4d ==164 / 15................(8)
From (6) above we get:
a + b +c + d + 121/15==43 / 3
a + b + c + d ==94 / 15........................(9)
Subtract (8) from (9) above:
- 5d ==14/3
d == - 14 / 15
Continue with this procedure for all 5 equations above and should get:
a=(91 / 15); b=(76 / 15);c= (-59 / 15); d=(-14 / 15); e=(121 / 15)
