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# system

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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

Jun 21, 2023

#1
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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)

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)

Jun 22, 2023